Introduction to Mechanics

Good day, grade 11 Dysians. Welcome to General Science. This is the second masterclass on physics and this is all about introduction to mechanics. To start, let us first define what is mechanics and how it is as a branch of physics. Let's see. So mechanics, according to this slide, this is a branch of physics that studies three different but are interconnected things. Mechanics wants to understand the motion of objects. It wants to quantify the movement of the objects. The first one, motion, paggalaw ng mga bagay. Gustong arali ng mechanics ang paggalaw ng mga bagay. Aside from knowing, aside from determining the... the quantity or the descriptions of motion of objects, mechanics also want to understand the forces that cause those motion. So aside from the motion of objects, aside from the movement of objects, mechanics wants to understand kung bakit siya gumalaw. And kaya siya gumalaw, that's because of the force. That's because of the puwersa. At yung puwersa na yun, Siya yung dahilan kung bakit gumalaw or nagbago yung galaw ng isang bagay. And aside from movement and forces, mechanics also wants us to understand conditions for stability. Kailan naman magiging stable yung paggalaw? Kailan naman magiging stable or at rest yung isang object? So that's mechanics. May tatlo siyang inaarad. It also answers questions like How fast is something moving? So it can give you a quantitative description of how fast is something moving that's based on the motion of objects. Bakit siya nag-accelerate? Bakit siya buibilis? Forces that cause or change those motion. And what forces are acting on it? Ano yung bagay? Ano yung mga force na nagiging dahilan kung bakit gumagalaw siya? Ano yung mga forces na nagbabalance out? Kaya siya nagiging stable. So, ito yung mga questions na pwede nating masagot because of mechanics. And actually, ang mechanics ay nahati pa sa tatlong sub-branches. So, again, to clarify, the umbrella term at this point is physics. Marami siyang branches. Okay? Isa doon ang mechanics. At sa mechanics, there are three sub-branches pa. May tatlong sangay pa siya. And those are these. The branches of mechanics. So we have kinematics, dynamics, and statics. For kinematics, ito yung first part, motion of objects. Kinematics describes kung paano gumagalo yung bagay. Okay, how objects move. And paano siya gumagalo in terms of its speed. Gaano siya gumagalaw in terms of its velocity or in terms of acceleration? So later on, maintindihan natin yung differences nung tatlong ito, nung speed, velocity, and acceleration. But here in kinematics, yun lang siya, quantitative description lang siya sa paggalaw ng object. There's no concept yet of why they move. Yes, gumalaw siya, for example, gumalaw siya ng 60 kilometers per hour. Pero bakit siya gumalaw? that's 60 kilometers per hour. Hindi pa siya nasasagot ng kinematics. Ang nakakasagot kung bakit gumagalaw yung objects ay dynamics. Okay? So, sa dynamics, dito naka-under yung forces that cause or change the motion. So, it explains why objects move, focusing on the forces and torques involved. And actually, ang Newton's Laws ay dito yung na-aral sa dynamics. Because if you look at Newton's law, first law is inertia, second law is force is equal to mass times acceleration, third, if there's an applied action, there's an equal and opposite reaction. Those are forces and forces. There's something involved in that. And they explained why things worked. That's dynamics. And the third one is statics. Statics studies objects at rest. or in equilibrium. Bakit siya ngayon equilibrium? Other term for equilibrium is balance. So what are the forces that act upon dun sa object na yun kung bakit siya stable? kung bakit siya balanced, kung bakit at rest siya. So those are the three branches of mechanics. So to give you an example, for instance, let's have a car accelerating on the road. If that's the situation, kinematics can give you an idea how they move, how the car moves, okay? So it can describe the car speed that increases from zero, let's say, yung kot siya ay nakaparada, tapos in 60 seconds ng paggalaw niya, 60 kilometers per hour na siya. So it can give you, yes, the speed, the acceleration, the velocity, because of kinematics. Quantitative descriptions. But dynamics will give you an idea why the car accelerates. Bakit siya bumilis? Maybe dahil nga nakaparada siya, tapos nung nag-start yung engine, yung force from the engine ay natransmit doon sa mga gulong, and which pushes against the road. Because, diba, thanks to friction, may mga resistance din sa paggalaw. And that's why, diba, kapag madulas ang kalsada, medyo prone sa accident because ang friction ay medyo nagiging mas mahina. Kasi parang nagiging slippery yung road. That's because of In a sense, friction But friction is the resistance To movement It pushes Against the road And because of that For example The car is moving here The friction is different And with that, it causes Of course, the friction is more intense It causes more acceleration or friction in the movement of the object. And therefore, it causes forward acceleration according to the Newton's second law. So, that's the dynamics. It can give you an idea of what are the forces that are there. Why is it moving? Or why is it moving slowly? Maybe because the friction is increasing. So, that's it. The impact of friction is increasing. So, basta in terms of forces, dynamics na makakapag-discuss niyan. Third one is statics. So, statics, nagpapasok naman natin siya if, for instance, yung car ay nakaparades sa isang hill. Meron diyan parang burol, tapos dito mo pinark yung car mo. Ano dapat yung mga forces na magbabalance out diyan in order for the car to become stable at the top of the hill? Okay, dito sa taas ng hill na to. So that it doesn't go up and down here or up and down here. So we need to understand it. So that it doesn't go wrong. So statics is the idea that we can give to ourselves. So those are the three branches of mechanics. Which is, mechanics are under physics. Later on, we will discuss those three branches of mechanics in detail. But before that, let's have... first, no, an idea of what are scalars and vectors. Remember, in the first masterclass, we've discussed physical quantities. And physical quantities, no, it describes, physical quantities describe natural phenomena. And para mag-make sense yung physical quantities, kailangan merong magnitude and its corresponding unit. Okay? That's the basic quantity. And actually, ang tawag doon sa quantity na yun is the scalar quantity. A scalar quantity is a quantity that is described by its magnitude. Magnitude is the number and its corresponding unit. So, syempre, hindi mag-mimix it, for example, yung 5, ano ba yung 5 na yun? 5 seconds ba? 5 kilograms ba? 5 meters ba? Kailangan nakadefine ano yung unit. So for example, you have 5 kilograms, that means, may idea ka na, ito ay mass. Okay, mass ito. Kapag binigay naman sa'yo ay in terms of seconds, oras to. Mayintindihan mo agad yung magnitude na may number and unit at hindi mo na kailangan ng direction niya. Okay, hindi naman sinasabi na mass 5 kilograms to the east. No, talagang 5 kilograms lang siya. Yung time naman. Moving forward lang naman yan. So there's no need to say the direction of time. So therefore, they are scalar quantities. These quantities can be described by its magnitude, the number, and its corresponding unit or symbol. The next one is vectors. Vectors are quantities that specify both magnitude and direction. In order for you to understand that quantity, there needs to be direction. Okay? So vectors involve directions. So for example, here you have the primary directions here, the north, east, south, and west. So you will see that there are two arrows. The red arrow is pointing to the east and therefore, the first unit, for example, you measure its length, that's 45. And it's 45 meters to the east. Okay? It goes to the east. Pwede mong sabihin na distance covered. Okay? Parang ganun. Or kaya, ito yung length. No? Noong, ano, and going to the east siya. Displacement. No? So titignan natin later on. Ano yung distance, ano yung displacement. Now, kung next one naman, for instance, you have another 45 meters sa green arrow. Ito yung sinulatan ko ngayon. And hindi naman siya going to the east. So, kailangan ma-specify mo the direction na at an angle siya. And sabi dito, 26 degrees north of each other. There's no need for you to bring a protractor, no? Pinakita lang natin na may iba't-ibang directions. Pwede siyang at to the east, to the north, to the west, to the south, or pwedeng nasa pagitan ng dalawa, pwedeng at an angle. So, kailangan mo ma-define yung angle. Okay? But basically, regardless of... that, direction siya. Kailangan mo i-specify yung direction. Okay? Sige. So with that, let's try to understand if these quantities na naka-flash ngayon sa slides ay scalar or vector. Before I reveal the answer, you can pause this video para masagutan niyo at your own. Pero in 5 seconds, I will try to answer this. So you can pause this video. Okay, so hopefully, nasagutan na yung anim na ito. So, titignan natin if these are scalar or vector. Okay? So, punta muna tayo dun sa mga scalar quantities. Okay? So, actually, length, as we know, kanina, binanggit na natin ng mass, binanggit na natin ng time, at isa sa mga kapatid na na-length, there's no need to specify direction. And therefore, length is a scalar quantity. At kung babalikan mo, Ang volume ay nanggaling lang sa length times width times height. And therefore, volume is also scalar quantity. Later on, sa lesson number 2 niyo sa loob ng classroom, may kita mo na ang density, parang ganyan, that's rho, R-H-O, Greek symbol, ay equal lang siya sa mass. over volume. And therefore, since both of them are scalar, density is also scalar. Force according to the Newton's second law of motion, force is equal to mass times acceleration. Mass is scalar, however, acceleration is not. Acceleration is vector. Later on, may kita natin why is it a vector quantity. Therefore, Force is a vector quantity. Gravity being a type of force is also a vector quantity. Why? Because, right? Gravity pulls the object downwards, towards the earth. Okay? But there's also a direction going up. That's against the gravity. So, you need to specify the direction. Same as with force, right? Does it go to the east, to the west, or such? And lastly, momentum. Momentum actually describes the quantity of the motion. And momentum is equal to mass times velocity. And velocity, later on, we will see that it is a vector quantity. And therefore, momentum is also a vector quantity. So hopefully, we got the right answers here. So now, we have the skills of identifying what are scalar quantities, what are vector quantities. So now I can proceed to the kinematics. discussion. Okay? So again, kinematics, ito yung nag-describe how objects move in terms of different parameters. Okay? So let's first discuss what motion is. Motion is basically the change in an object's position based on its reference point or based on the origin. So for example, we were in Sapientia And I walked from here in front, here in one tile in front of this, then I went to the middle. If this is my reference point, and you can see that I walked to this, and this is my final position, there is motion. Because there is change in object's position. Motion can be translational or rotational. What does this mean? When we say translational, related siya sa term na linear. When we say rotational, pwede siyang naka-circular pa. Kaya yung motion ay pang ikot-ikot. Pwede yung linear, katulad nito sa example natin. So basically, when we say motion, there's a change in the position of the object. And isa sa mga laging pinagtatalunan ay yung distance. concept of distance and displacement. Okay? So actually, binigay na dito yung definition. Distance is the total length of the path taken and distance is scalar while displacement only depends on the starting and final position, not on the actual path taken. And this is a vector. Pero para may sa pang-tindihan natin, I will give an example. For example, naglakad nga ako from Sapiensa. For example, I'm a student. nag-recess. So, lumabas ako ng sapyansya. Pinuntahong ko yung kaibigan ko sa ibang classroom. So, naglakad ako, for instance, ng 20 meters. Tapos, pumunta kami sa canteen. Let's say, naka-13 meters kami. Okay? So, yun. Tapos, dito sa example na to, pwede natin makita anong distance na na-cover niya. So, in terms of distance, ang definition natin ng distance is the total path covered. So, basically, lahat ng pinuntahan mo ay parte ng distance. Regardless kung ano yung original and final position mo, basta. Kasama siya sa path, that's distance. Regardless of the direction. Regardless of anything. Basta yung path na tinahap. Kaya siya scalar. Kasi walang impact masyado yung direction sa kanya. So distance, so yan dito. 20 plus 13, so that's 33 meters. So parang ganyan. However, displacement on the other hand, ang gusto niya lang, ay yung difference ng final and starting points or starting positions. Final minus starting points. So paano ibig sabihin nun? Pwede nating i-paraphrase yung salit ng displacement by saying that this is the shortest distance from the starting point to the final point. And dito kung titignan mo, ano yung possible na displacement dyan? The possible displacement or the shortest distance would be the straight line or diagonal. Right? Because if you travel 20 meters here, then 13 meters here, then 33 meters here, but actually there's a shortcut. So, the displacement is like that. Shortest distance that can be covered. And this has an impact and direction on it. So, displacement is actually a vector quantity. So, sir, paano mo susuka to? If you are interested, you can see na may right triangle ka magubo. So, this is the hypotenuse of a triangle. Diba? And, kategorian theorem to. Kung gusto mo lang namang isolve, but we'll not solve that here sa jet side. Okay? So, yun yung pwedeng gawin nating kwento. For kaya naman, pwede rin naman, ganito yung example. So, what if, yun nga, nasa canteen tayo. tapos, bumalik ka na ngayon or nag-CR muna kayo ng friend mo. So, dito, for example, ayan, 18 meters. Okay? Naglakad kayo ng 18 meters ulit. Kunwari lang ito. Tapos, bumalik na kayo sa piyensya after. So, bumalik kayo dito. Sabihin natin na nga nasa 15 meters. 15, okay? So, based on the path na tinahak mo, no, ilan lahat sila? Kung tama ba, 33? 33, so 66 meters ang distance mo. Kasi, yun ay lahat ng path na pinahak mo. That's part of your distance. On the other hand, yung displacement, again, ay based sa final minus starting position. Nagsimula ka sa position na to, nagtapos ka sa position na yan, and therefore, the displacement is zero. Okay? Kasi dun ka rin pumunta. Distance is non-zero, displacement is zero kapag ka buhabalik ka dun sa original position mo. So distance, scalar, displacement, vector. Ito lang actually din yung sinasabi natin earlier. Kung mapapansin nyo sa figures dito, figure number one, from the position 0.1 to 0.2, the path taken is this. So that's the distance because distance wants you to describe the total length of the path. taken but the displacement is the shortest distance so why would you go around here if there's a shortest distance here that's your displacement only depends on the starting and the final position aside from this this is for example your original position and then there's your path taken but you um you went back to the original position so the distance is all the path you've taken, but the displacement is zero because you went back to the original position. So your final and starting positions are the same. So there's no displacement. Okay, I hope that's clear. Because of the distance and displacement, we can now actually define and describe other parameters involved in kinematics. But first, there are different types of motions. mentioned earlier, there's translational, there is rotational, and translational motion is also coined as rectilinear motion, or rectilinear motion is under translational motion. So this is a motion along a straight line, and this is one-dimensional only, so very linear. And there are parameters that can describe motion under this type of motion. So we have speed. Speed is basically distance per unit time. So if you are to compute for speed, speed, distance over time, okay? Distance, as we know, is scalar. Time is also scalar. Therefore, speed is scalar. Okay? Pagbabago sa distansya per unit time. That's speed. Velocity, on the other hand, includes displacement as its numerator. Therefore, velocity describes the change in an object's displacement per unit time. And displacement is vector. And therefore, velocity inherits the vector. identity of this parameter displacement and therefore velocity is vector. And lastly, acceleration is the change of an object's velocity per unit time. So we can see that they have different denominators from just distance, the actual path taken, displacement, the shortest distance or the difference between the final and the starting points, and velocity being the change in the displacement per unit time. So, it's just acceleration. And since velocity is vector, acceleration inherits that identity. So, therefore, acceleration is also a vector quantity. Okay? So, we can better understand this by understanding, for instance, position time graphs. Okay? So, position is marked as x. Time is t. Okay? And here, the y-axis, the one. that is in terms of vertical lines, the Y-axis. is the position and the horizontal axis or the x axis is time okay so please take note of that those always when you have graphs you first read the labels of the x and y axis to better understand the graph so if you have this image uh as you can see here uh the time moves okay for example if this is zero 1, 2, 3, 4, 5 seconds. Okay? So, the time is moving, but the position is not. For example, it's still there at 3 meters. It's not moving. Or it's still in position number 3, it's not moving. So, it means, if that's your position time graph, the object is at 3. It's not moving. Even if the time is moving, there's no change in position. Therefore, the object is at 3. You can describe that as that. Okay, next. The second graph shows that time constantly moves and the position also constantly moves, increasing steadily. So if it is increasing steadily, we can say that object moves. Yes, the object moves. It changes the position, right? There's motion. And we can say that the object is moving with constant speed or constant. velocity. But in this case, since there is position here and it increases steadily, we can say that that's constant velocity. Next one, same as with the second graph, the line increases, but it is not steadily increasing. As you can see here, the time changes. The position also changes with respect to time. However, the position increases slowly at the start and it moves faster at the second part of the graph. Meaning, there is an acceleration from a slow motion to a faster motion. And therefore, object is moving with constant acceleration. So you can understand or you can actually interpret graphs, and you can formulate interpretations afterwards. By understanding first or by knowing first what are the x and y-axis, so that you can know what the lines mean. So aside from the position time graph, I have here the velocity time graph. Velocity symbolizes letter V. Time is letter V. 30 and velocity is in the y-axis, time is at the x-axis. As you can see here, there's a green line over here at this part. Time changes but the velocity is not increasing nor decreasing. Therefore, we can say that the object is at rest because that's velocity. Velocity is equal to the change in the displacement per unit time. There's no changes in the velocity, therefore there's no movement. The object is at rest. The next one, as you can see here, time also changes. Velocity now is non-zero. Non-zero. So therefore, the object is not at rest, but it is in terms of constant velocity. It moves through constant velocity. And therefore, The velocity here, I mean, the y component here is constant because the velocity is constant. And lastly, we have here the third graph. So again, the time changes, but the velocity also changes. And if there's changes in velocity per unit time, there is an acceleration. object is moving with acceleration. So I hope by now you can understand these time gaps. There are some exercises here. You can try to answer this. You can read first the content of the slide and then pause this video. After five seconds, I will try to answer this. But again, in order for you to test your understanding of the lesson, you pause this video and then I'll count until five. then I'll answer the questions. So I hope by now you have your answers already. Then you pause this video. Let's try to answer this. Given the following position time plots, so there's position time plots, answer the questions below. So first one, which pertains to an object with constant speed? Again, we're talking about position time graph. Therefore, if there's a constant speed, the position must steadily increase. And as you can see in the four plots that we have, only letter B has a constant or a linear increase or changes in the position. And therefore, the answer is letter B. Okay, next one. Which pertains to an object that reverses direction? What do we mean by that? Okay, so we can have a graph that in terms of position, it goes up. And then if it reverses direction, it goes down, moving nearer to its original position. And actually, there's a graph pertaining to that, and that's letter A, right? Because as you can see, if this is the starting position, the time increases. But this part of the curve, it goes away to its original position. But at this point, it reverses direction and maybe after some time, it goes back to its original position. Okay? As the time changes. So, that's the answer. And lastly, which pertains to an object that starts slowly and then speeds up. So, the manifestation of an object that starts slowly, the increase of the first one is not that fast. And then, after some time, it gets faster and faster. And actually, that pertains to letter D. Kasi mabagal siya sa umpisa, mataas yung pag-increase niya sa dulog. So I hope nakuha ninyo yung lamang sagot. Okay? Next. There are also questions here. Again, you can try to answer this. You can pause this video. And after five seconds, I'll try to answer. So I hope by now you have your answers with you. This plot is again a position time graph. And the questions are presented here. In which of the labeled points is the velocity of an object, for instance, 0, constant in positive, constant in negative, increasing in magnitude, and decreasing in magnitude? So here are the answers. Why is that? First one, the velocity of an object is 0 at point 4. Because as you can see here, there is no change in the position. At this point, there's no change in the position. Therefore, no velocity is present here. There's zero velocity here at point 4. Because if you noticed, the line was flat. Its position did not change at that particular point. Therefore, there's zero velocity. Okay? Next one. Sa constant and positive naman, bakit kaya itong si 1? Kasi, kumapansin mo, at this point 1, linear yung pag-increase niya, therefore, constant increase in terms of velocity, and positive siya, kasi pataas yung kanyang movement. Therefore, point 1 is the point wherein the velocity is constant and positive. Next one, ano naman daw yung point na constant and negative? Kitang-kita naman, na very linear tong sa 0.5 na to. Okay? And bakit siya negative? Kasi instead, kasi if you are moving away from your position, that's positive. But if you are going back to where you've started, at least at this point or at the origin, it's negative. Pababa ka kasi. Okay? So, Constant and negative is 0.5. Next, increasing in magnitude. What happens if the velocity is increasing in magnitude? If you remember earlier, in the position time graph that we have, when it became, here, let's go back. In the position time plot, right? The one that is not linear but curved. may possibility of an acceleration. And that's because nag-increase or nag-decrease yung magnitude ng velocity. So dito, increasing in magnitude yung sa 0.2, kasi tinignan mo, hindi siya linear. And talagang mataas yung slope. And therefore, kung mataas ang slope, sa maikling panahon, sa 2 to 4 minutes, mataas ang increase or pagbabago niya sa position. Therefore, increasing in magnitude. At ano naman yung area na decreasing in magnitude? Kung napansin mo naman, after niyang tumaas ng very steady and very high, dito sa point 3, bumagal siya. At a particular time, ang bagal ng pagbago ng position until mag-zero yung velocity sa point 4. Therefore, sinin nagdi-decrease in magnitude dun sa point 3 nagsimula. Okay? So I hope at this point, ang skill na meron tayo is marunong na tayong mag-interpret ng mga plots. So, you can also try to answer this. At which point does the object have the highest displacement? Okay? So, displacement is again final minus the starting point. I'll give you three seconds. The answer is letter B. Kasi dito sa point na to, malayo siya doon sa original position niya. Okay? Siya yung may pinakamala yung pwesto sa kanya original position. So the answer is letter B. Next, at which point is the object at rest? Hindi nagbago yung posisyon? Saan kaya yun? Kitang-kita natin, ano? Pwede siyang... Sige, I'll give you pala 3 seconds to answer. Kitang-kita natin na hindi siya gumalaw yung posisyon saan? Sa point E. No? Hindi gumalaw siya. nagplatu yung position. And at the same time, hindi lang siya masyadong kita, pero pwede rin nating sabihin na nagplatu din siya dito sa point B. May area na kung saan nagplatu yung curve. Same as true with D. And therefore, may pagkakataon din sa B at sa D ay nagrest yung object. But the best answer here is letter E. Next, at which point is the object fastest? Ibig sabihin, Saan siya mabilis nagbago ng position? I'll give you three seconds. The answer is letter C. Kasi kung nakita mo dito, ang grabe yung in-increase niya ng position. Ay, in-increase, sorry. Changes niya in position. From a positive position to a negative position. Sir, ano yung ibig sabihin ng positive saka negative position na yan? Pwede nating sabihin kung ganyan siya. Positive siya kapag going north. Negative siya if going south. Pwedeng ganun ang interpretation natin dyan. Positive siya if going east. Negative siya if going west. Okay? For example, dito sa B, nandito siya sa may north. Tapos umalis siya dun sa north, papuntang south naman. Okay? Kaya managahal ng positive or negative positions. Buhabalik din siya para ngayon. Okay? So hopefully, naintindihan. ang papag-interpret ng mga plots. Next, acceleration. How do we define acceleration earlier? That's the change in velocity per unit time. At ang velocity, may dalawang components yan. Nandyan ang speed, pero mayroon ding direction. So, acceleration can mean that there's a change in speed or a change in direction or a change in both. Okay? There's also an acceleration if the... direction of the speeding up is also in line with the direction of the velocity. As you can see here in this figure, the car is moving here, so the velocity is moving to the east, going to the east, and the acceleration, the changes that you are trying to have, is also going to the east. So if you're... Acceleration is in line with the direction of the velocity. Therefore, the car will speed up. Okay? So, it will be fast. But if the case is different. For example, the car will go to this side. But you pressed the brake. So, therefore, there was friction. The impact of friction increased. So, now, the acceleration will go to this side. So if that's the case, babagal ngayon yung Because velocity and acceleration have different directions. But if it accelerates rather at an angle to velocity, for example, your velocity is here, and your acceleration is going here, the instance can be made in a different direction. So, it can be like that. Okay? So, that's acceleration. Velocity over time. Okay? So those are the parameters that can help us describe how objects move. Other types of motion include free fall. Basically, when we say free fall, there's only vertical motion. Ibig sabihin ng vertical motion, ito lang. Taas baba lang. motion na pwedeng ma-apply dyan. And usually, it goes down because of gravity. The gravitational pull of the Earth. Okay? So, here, you have some facts about the free fall, free falling objects. The gravitational pull of the Earth on an object results in a falling motion, pababang motion. Kung mapapasin mo, no? If you, taw dito, allow a billiard ball, to fall freely. If you notice where it started, it's a bit slow, but, um, people here, photographs will reveal that it's very fast. That it's very fast after some time. That's because gravitational acceleration. We have uh, speed in the drop of gravity down. And actually, on Earth, that is 9.8 meter per second squared. yung pag-accelerate niya. Yung pagbulusok niya pababa. That's 9.8 meter per second squared. The acceleration of an object varies with the distance of the object from the Earth's surface. Kaya ngayon, ginagawa natin constant. Na 9.8 meter per second squared, basta nandito sa Earth. Aside from that, the acceleration of an object does not vary with the mass of the object, at least at this point. Hindi siya... hindi siya nakaka-apekto sa gravitational acceleration, and any falling body will experience air resistance slowing down its motion. Yung air resistance, ito yung parang pumipigil sa pagbagsak. Diba? Parang yung feather. Ang feather, kapag may buhabagsak na feather or balahibo, diba, mabagal yung kanyang paggalaw or pagbaba kasi there's an air resistance. May pumipigil doon sa balahibo to go down easily. But in terms of free fall, We need to have assumptions so that we don't have a hard time. We must neglect air resistance. Okay? We define now free fall as the constant acceleration of a body falling under the influence of Earth's gravitational attraction. It means that the movement is vertical. The movement is vertical. And the acceleration due to gravity is 9.8 meters per second squared. It's positive if it goes down because Okay. Pabilis ng pabilis yung pagbuluso. Kaya positive. But if it goes up, it is negative kasi against ka sa gravity. So that's free fall. Okay? Meron siyang relative, which is projectile motion. Or projectile motion. Ito, may involvement pa rin of gravity. However, this motion is characterized by simultaneous vertical things to gravity and horizontal movement. because of the angle when you throw the ball. So, for example, you throw the ball, for instance. For example, you throw an object at this point, you place it at an angle, it has a trajectory, or it has a path that it runs. So, what is called a path taken by the projectile is its trajectory. But again, In terms of projectile motion, it is only influenced by gravity. So talaga may vertical movement. And at the same time, because it is at an angle, may horizontal movement din siya. As you can see here, there is an independence of X or the horizontal movement in Y, the vertical movement. There are two. uh objects here one is a red ball the second one is a yellow colored ball but yeah the red ball was, what do you call it, was dropped in terms of free fall because, look, it's vertical. It's just a vertical movement. Down. And then, the yellow ball was dropped at an angle. There's a projectile. So, it's not just vertical down, but there's an angle. But if you notice, in the photographs, even if you say they have a different way of falling, At this particular time, they're both here. They're the same y-axis. At this time, they're still the same. So, what does that mean? At any given time, both balls have the same y-position or y-axis and y-velocity despite having different x-positions and x-velocities. So, therefore, because the x and y are different, naman palang X and Y We can separate the computation of horizontal and vertical parts of a projectile. Because we said that a projectile is not just vertical like a free fall. It has vertical thanks to gravity and horizontal movement thanks to an angle when you throw an object. In general science, we cannot complete that. But that's it. Ang projectile may vertical sa horizontal components. Next, we have uniform circular motion. Uniform circular motion, from the name itself, it is the motion along a circular path with constant speed. Constant yung kanyang speed. Anong pinagkaiba? Bakit kaya ang velocity is always changing? It's because dahil bilog siya, Kahit nasabihin mong constant speed siya, kailangan niya mag-change ng direksyon. Kasi, for example, ito yung bola, kapag hindi siya nag-change ng direksyon, gaganyan siya. Hindi siya magiging circular. So, therefore, kailangan niya magbago ng direksyon. At sa pagbago niya ng direksyon, maapektuhan ang velocity, being a vector quantity, and acceleration, na kailangan din ng direksyon. Okay? So, Velocity and acceleration both have constant magnitudes kasi nga same yung velocity, constant, I'm sorry, constant rather yung speed. Pinagkakaiba is may pagbabago sa directions. So that's uniform circular motion. And dito sa uniform circular motion, mayroon tayong tinatawag na centripetal force and centripetal acceleration. Centripetal force is a center-seeking force. Ito yung dahilan kung bakit nagsistay sa bilog yung objects. So, for example, yung car na umiikot pa bilog, may tendency naman siya to go out of the circular path. But because of centripetal force that goes, papunta sa center, it keeps the object moving along a circular path. At dahil, nasa circular path siya, may pagbabago sa direction every time na umiikot siya ng bilog. At dahil may pagbabago sa direction, masasabi natin that there is an acceleration. Okay? So there is an acceleration. So there are examples of centripetal forces. So later on, we will discuss this. Yung tension, gravity. and friction. Why did they become examples of centripetal forces? But also, you can search, you can do research, why are these examples of centripetal forces? Last slide, for this part of the masterclass, we have torque. Torque basically is a twisting force. Okay? And because it's a twisting force, It allows rotation. But basically, for us to understand torque, alam naman natin siguro na may pinto. This is an example of a door. Torque is situated here sa may hinge. Alam nyo yung hinge yung sa pinto. Diba sa pagitan ng pinto, tapos yung frame ng pinto, meron niyang parang, yan, yung nagkakos ng movement. Okay? Parang mga turnilyo. Diba may mga turnilyo sa part na yan. Tapos, You won't see a door that the doorknob is near this region or this twisting area. Lagi ang doorknob nandun sa kabilang dulo. Because, di ba, kapag nagbubukas at sara tayo ng pinto, saan tayo nag-a-apply ng force? Nag-a-apply tayo ng force doon sa doorknob. So, ano sinasabi ng torque? Para daw ma-ensure na mas mataas yung twist, kailangan yung object na pinag-a-applyan mo ng force ay malayo sa torque or malayo sa hinge. Okay? Dapat may distance. Atatawag dun sa distance na yun ay lever arm. Okay? Lever arm. So the higher or the longer the lever arm at may ina-apply kang force, mas mataas yung torque and therefore, mas mabilis or mas madaling it twists yung pinto. Kaya nabubukas at saran mo siya. Kasi kapag dito mo nilagay yung doorknob, Pag dito mo nilagay yung doorknob, dahil napakalapit niya doon sa hinge, ang liit nung lever arm. Ang liit nung lever arm mo. Or ang liit nung distance between the hinge and doon sa doorknob, which, again, doon tayo nag-a-apply ng force. And therefore, mababa to, mababa din ang torque. Therefore, maliit lang yung twisting force. So, kailangan mo mag-exert ng sobrang taas na force para lang ma-twist mo yung... So, that's the reason why the door knob is far from the hinge. Or, it's like there are screws. That's because, if it's far, there's only a little force that you need to exert in order for you to twist those hinges or those screws. Okay? Question so far? So if you have questions, please write it down sa mga notes ninyo. Or you can also write your questions sa ating comment section dito sa video na ito. And we will try to answer those ating next na face-to-face masterclass. So I hope you've learned something about kinematics. Nakita natin that there are different parameters to describe how objects move. There are also different types of motion. Okay? So in the next masterclass, we'll focus on the remaining two branches of mechanics. We'll discuss dynamics and statics. Thank you so much for watching this video. Goodbye. See you next time.

Good day, grade 11 Dysians. Welcome to General Science. This is the second masterclass on physics and this is all about introduction to mechanics.

To start, let us first define what is mechanics and how it is as a branch of physics. Let's see. So mechanics, according to this slide, this is a branch of physics that studies three different but are interconnected things.

Mechanics wants to understand the motion of objects. It wants to quantify the movement of the objects. The first one, motion, paggalaw ng mga bagay.

Gustong arali ng mechanics ang paggalaw ng mga bagay. Aside from knowing, aside from determining the... the quantity or the descriptions of motion of objects, mechanics also want to understand the forces that cause those motion.

So aside from the motion of objects, aside from the movement of objects, mechanics wants to understand kung bakit siya gumalaw. And kaya siya gumalaw, that's because of the force. That's because of the puwersa.

At yung puwersa na yun, Siya yung dahilan kung bakit gumalaw or nagbago yung galaw ng isang bagay. And aside from movement and forces, mechanics also wants us to understand conditions for stability. Kailan naman magiging stable yung paggalaw?

Kailan naman magiging stable or at rest yung isang object? So that's mechanics. May tatlo siyang inaarad. It also answers questions like How fast is something moving?

So it can give you a quantitative description of how fast is something moving that's based on the motion of objects. Bakit siya nag-accelerate? Bakit siya buibilis?

Forces that cause or change those motion. And what forces are acting on it? Ano yung bagay? Ano yung mga force na nagiging dahilan kung bakit gumagalaw siya? Ano yung mga forces na nagbabalance out?

Kaya siya nagiging stable. So, ito yung mga questions na pwede nating masagot because of mechanics. And actually, ang mechanics ay nahati pa sa tatlong sub-branches. So, again, to clarify, the umbrella term at this point is physics.

Marami siyang branches. Okay? Isa doon ang mechanics.

At sa mechanics, there are three sub-branches pa. May tatlong sangay pa siya. And those are these. The branches of mechanics.

So we have kinematics, dynamics, and statics. For kinematics, ito yung first part, motion of objects. Kinematics describes kung paano gumagalo yung bagay. Okay, how objects move. And paano siya gumagalo in terms of its speed.

Gaano siya gumagalaw in terms of its velocity or in terms of acceleration? So later on, maintindihan natin yung differences nung tatlong ito, nung speed, velocity, and acceleration. But here in kinematics, yun lang siya, quantitative description lang siya sa paggalaw ng object. There's no concept yet of why they move.

Yes, gumalaw siya, for example, gumalaw siya ng 60 kilometers per hour. Pero bakit siya gumalaw? that's 60 kilometers per hour. Hindi pa siya nasasagot ng kinematics.

Ang nakakasagot kung bakit gumagalaw yung objects ay dynamics. Okay? So, sa dynamics, dito naka-under yung forces that cause or change the motion.

So, it explains why objects move, focusing on the forces and torques involved. And actually, ang Newton's Laws ay dito yung na-aral sa dynamics. Because if you look at Newton's law, first law is inertia, second law is force is equal to mass times acceleration, third, if there's an applied action, there's an equal and opposite reaction. Those are forces and forces.

There's something involved in that. And they explained why things worked. That's dynamics.

And the third one is statics. Statics studies objects at rest. or in equilibrium. Bakit siya ngayon equilibrium?

Other term for equilibrium is balance. So what are the forces that act upon dun sa object na yun kung bakit siya stable? kung bakit siya balanced, kung bakit at rest siya. So those are the three branches of mechanics. So to give you an example, for instance, let's have a car accelerating on the road.

If that's the situation, kinematics can give you an idea how they move, how the car moves, okay? So it can describe the car speed that increases from zero, let's say, yung kot siya ay nakaparada, tapos in 60 seconds ng paggalaw niya, 60 kilometers per hour na siya. So it can give you, yes, the speed, the acceleration, the velocity, because of kinematics.

Quantitative descriptions. But dynamics will give you an idea why the car accelerates. Bakit siya bumilis? Maybe dahil nga nakaparada siya, tapos nung nag-start yung engine, yung force from the engine ay natransmit doon sa mga gulong, and which pushes against the road. Because, diba, thanks to friction, may mga resistance din sa paggalaw.

And that's why, diba, kapag madulas ang kalsada, medyo prone sa accident because ang friction ay medyo nagiging mas mahina. Kasi parang nagiging slippery yung road. That's because of In a sense, friction But friction is the resistance To movement It pushes Against the road And because of that For example The car is moving here The friction is different And with that, it causes Of course, the friction is more intense It causes more acceleration or friction in the movement of the object. And therefore, it causes forward acceleration according to the Newton's second law.

So, that's the dynamics. It can give you an idea of what are the forces that are there. Why is it moving? Or why is it moving slowly? Maybe because the friction is increasing.

So, that's it. The impact of friction is increasing. So, basta in terms of forces, dynamics na makakapag-discuss niyan. Third one is statics. So, statics, nagpapasok naman natin siya if, for instance, yung car ay nakaparades sa isang hill.

Meron diyan parang burol, tapos dito mo pinark yung car mo. Ano dapat yung mga forces na magbabalance out diyan in order for the car to become stable at the top of the hill? Okay, dito sa taas ng hill na to.

So that it doesn't go up and down here or up and down here. So we need to understand it. So that it doesn't go wrong. So statics is the idea that we can give to ourselves. So those are the three branches of mechanics.

Which is, mechanics are under physics. Later on, we will discuss those three branches of mechanics in detail. But before that, let's have... first, no, an idea of what are scalars and vectors.

Remember, in the first masterclass, we've discussed physical quantities. And physical quantities, no, it describes, physical quantities describe natural phenomena. And para mag-make sense yung physical quantities, kailangan merong magnitude and its corresponding unit. Okay? That's the basic quantity.

And actually, ang tawag doon sa quantity na yun is the scalar quantity. A scalar quantity is a quantity that is described by its magnitude. Magnitude is the number and its corresponding unit.

So, syempre, hindi mag-mimix it, for example, yung 5, ano ba yung 5 na yun? 5 seconds ba? 5 kilograms ba?

5 meters ba? Kailangan nakadefine ano yung unit. So for example, you have 5 kilograms, that means, may idea ka na, ito ay mass. Okay, mass ito.

Kapag binigay naman sa'yo ay in terms of seconds, oras to. Mayintindihan mo agad yung magnitude na may number and unit at hindi mo na kailangan ng direction niya. Okay, hindi naman sinasabi na mass 5 kilograms to the east.

No, talagang 5 kilograms lang siya. Yung time naman. Moving forward lang naman yan. So there's no need to say the direction of time.

So therefore, they are scalar quantities. These quantities can be described by its magnitude, the number, and its corresponding unit or symbol. The next one is vectors.

Vectors are quantities that specify both magnitude and direction. In order for you to understand that quantity, there needs to be direction. Okay? So vectors involve directions. So for example, here you have the primary directions here, the north, east, south, and west.

So you will see that there are two arrows. The red arrow is pointing to the east and therefore, the first unit, for example, you measure its length, that's 45. And it's 45 meters to the east. Okay?

It goes to the east. Pwede mong sabihin na distance covered. Okay? Parang ganun. Or kaya, ito yung length.

No? Noong, ano, and going to the east siya. Displacement.

No? So titignan natin later on. Ano yung distance, ano yung displacement. Now, kung next one naman, for instance, you have another 45 meters sa green arrow.

Ito yung sinulatan ko ngayon. And hindi naman siya going to the east. So, kailangan ma-specify mo the direction na at an angle siya.

And sabi dito, 26 degrees north of each other. There's no need for you to bring a protractor, no? Pinakita lang natin na may iba't-ibang directions. Pwede siyang at to the east, to the north, to the west, to the south, or pwedeng nasa pagitan ng dalawa, pwedeng at an angle.

So, kailangan mo ma-define yung angle. Okay? But basically, regardless of...

that, direction siya. Kailangan mo i-specify yung direction. Okay? Sige. So with that, let's try to understand if these quantities na naka-flash ngayon sa slides ay scalar or vector.

Before I reveal the answer, you can pause this video para masagutan niyo at your own. Pero in 5 seconds, I will try to answer this. So you can pause this video.

Okay, so hopefully, nasagutan na yung anim na ito. So, titignan natin if these are scalar or vector. Okay? So, punta muna tayo dun sa mga scalar quantities. Okay?

So, actually, length, as we know, kanina, binanggit na natin ng mass, binanggit na natin ng time, at isa sa mga kapatid na na-length, there's no need to specify direction. And therefore, length is a scalar quantity. At kung babalikan mo, Ang volume ay nanggaling lang sa length times width times height.

And therefore, volume is also scalar quantity. Later on, sa lesson number 2 niyo sa loob ng classroom, may kita mo na ang density, parang ganyan, that's rho, R-H-O, Greek symbol, ay equal lang siya sa mass. over volume. And therefore, since both of them are scalar, density is also scalar. Force according to the Newton's second law of motion, force is equal to mass times acceleration.

Mass is scalar, however, acceleration is not. Acceleration is vector. Later on, may kita natin why is it a vector quantity.

Therefore, Force is a vector quantity. Gravity being a type of force is also a vector quantity. Why?

Because, right? Gravity pulls the object downwards, towards the earth. Okay?

But there's also a direction going up. That's against the gravity. So, you need to specify the direction. Same as with force, right?

Does it go to the east, to the west, or such? And lastly, momentum. Momentum actually describes the quantity of the motion. And momentum is equal to mass times velocity. And velocity, later on, we will see that it is a vector quantity.

And therefore, momentum is also a vector quantity. So hopefully, we got the right answers here. So now, we have the skills of identifying what are scalar quantities, what are vector quantities.

So now I can proceed to the kinematics. discussion. Okay?

So again, kinematics, ito yung nag-describe how objects move in terms of different parameters. Okay? So let's first discuss what motion is.

Motion is basically the change in an object's position based on its reference point or based on the origin. So for example, we were in Sapientia And I walked from here in front, here in one tile in front of this, then I went to the middle. If this is my reference point, and you can see that I walked to this, and this is my final position, there is motion. Because there is change in object's position. Motion can be translational or rotational.

What does this mean? When we say translational, related siya sa term na linear. When we say rotational, pwede siyang naka-circular pa. Kaya yung motion ay pang ikot-ikot.

Pwede yung linear, katulad nito sa example natin. So basically, when we say motion, there's a change in the position of the object. And isa sa mga laging pinagtatalunan ay yung distance. concept of distance and displacement.

Okay? So actually, binigay na dito yung definition. Distance is the total length of the path taken and distance is scalar while displacement only depends on the starting and final position, not on the actual path taken. And this is a vector. Pero para may sa pang-tindihan natin, I will give an example.

For example, naglakad nga ako from Sapiensa. For example, I'm a student. nag-recess.

So, lumabas ako ng sapyansya. Pinuntahong ko yung kaibigan ko sa ibang classroom. So, naglakad ako, for instance, ng 20 meters.

Tapos, pumunta kami sa canteen. Let's say, naka-13 meters kami. Okay? So, yun. Tapos, dito sa example na to, pwede natin makita anong distance na na-cover niya.

So, in terms of distance, ang definition natin ng distance is the total path covered. So, basically, lahat ng pinuntahan mo ay parte ng distance. Regardless kung ano yung original and final position mo, basta. Kasama siya sa path, that's distance. Regardless of the direction.

Regardless of anything. Basta yung path na tinahap. Kaya siya scalar.

Kasi walang impact masyado yung direction sa kanya. So distance, so yan dito. 20 plus 13, so that's 33 meters.

So parang ganyan. However, displacement on the other hand, ang gusto niya lang, ay yung difference ng final and starting points or starting positions. Final minus starting points. So paano ibig sabihin nun?

Pwede nating i-paraphrase yung salit ng displacement by saying that this is the shortest distance from the starting point to the final point. And dito kung titignan mo, ano yung possible na displacement dyan? The possible displacement or the shortest distance would be the straight line or diagonal.

Right? Because if you travel 20 meters here, then 13 meters here, then 33 meters here, but actually there's a shortcut. So, the displacement is like that. Shortest distance that can be covered. And this has an impact and direction on it.

So, displacement is actually a vector quantity. So, sir, paano mo susuka to? If you are interested, you can see na may right triangle ka magubo. So, this is the hypotenuse of a triangle.

Diba? And, kategorian theorem to. Kung gusto mo lang namang isolve, but we'll not solve that here sa jet side.

Okay? So, yun yung pwedeng gawin nating kwento. For kaya naman, pwede rin naman, ganito yung example. So, what if, yun nga, nasa canteen tayo.

tapos, bumalik ka na ngayon or nag-CR muna kayo ng friend mo. So, dito, for example, ayan, 18 meters. Okay?

Naglakad kayo ng 18 meters ulit. Kunwari lang ito. Tapos, bumalik na kayo sa piyensya after. So, bumalik kayo dito. Sabihin natin na nga nasa 15 meters.

15, okay? So, based on the path na tinahak mo, no, ilan lahat sila? Kung tama ba, 33?

33, so 66 meters ang distance mo. Kasi, yun ay lahat ng path na pinahak mo. That's part of your distance.

On the other hand, yung displacement, again, ay based sa final minus starting position. Nagsimula ka sa position na to, nagtapos ka sa position na yan, and therefore, the displacement is zero. Okay?

Kasi dun ka rin pumunta. Distance is non-zero, displacement is zero kapag ka buhabalik ka dun sa original position mo. So distance, scalar, displacement, vector.

Ito lang actually din yung sinasabi natin earlier. Kung mapapansin nyo sa figures dito, figure number one, from the position 0.1 to 0.2, the path taken is this. So that's the distance because distance wants you to describe the total length of the path.

taken but the displacement is the shortest distance so why would you go around here if there's a shortest distance here that's your displacement only depends on the starting and the final position aside from this this is for example your original position and then there's your path taken but you um you went back to the original position so the distance is all the path you've taken, but the displacement is zero because you went back to the original position. So your final and starting positions are the same. So there's no displacement. Okay, I hope that's clear. Because of the distance and displacement, we can now actually define and describe other parameters involved in kinematics.

But first, there are different types of motions. mentioned earlier, there's translational, there is rotational, and translational motion is also coined as rectilinear motion, or rectilinear motion is under translational motion. So this is a motion along a straight line, and this is one-dimensional only, so very linear.

And there are parameters that can describe motion under this type of motion. So we have speed. Speed is basically distance per unit time.

So if you are to compute for speed, speed, distance over time, okay? Distance, as we know, is scalar. Time is also scalar. Therefore, speed is scalar. Okay?

Pagbabago sa distansya per unit time. That's speed. Velocity, on the other hand, includes displacement as its numerator.

Therefore, velocity describes the change in an object's displacement per unit time. And displacement is vector. And therefore, velocity inherits the vector. identity of this parameter displacement and therefore velocity is vector. And lastly, acceleration is the change of an object's velocity per unit time.

So we can see that they have different denominators from just distance, the actual path taken, displacement, the shortest distance or the difference between the final and the starting points, and velocity being the change in the displacement per unit time. So, it's just acceleration. And since velocity is vector, acceleration inherits that identity. So, therefore, acceleration is also a vector quantity.

Okay? So, we can better understand this by understanding, for instance, position time graphs. Okay?

So, position is marked as x. Time is t. Okay? And here, the y-axis, the one. that is in terms of vertical lines, the Y-axis.

is the position and the horizontal axis or the x axis is time okay so please take note of that those always when you have graphs you first read the labels of the x and y axis to better understand the graph so if you have this image uh as you can see here uh the time moves okay for example if this is zero 1, 2, 3, 4, 5 seconds. Okay? So, the time is moving, but the position is not.

For example, it's still there at 3 meters. It's not moving. Or it's still in position number 3, it's not moving.

So, it means, if that's your position time graph, the object is at 3. It's not moving. Even if the time is moving, there's no change in position. Therefore, the object is at 3. You can describe that as that.

Okay, next. The second graph shows that time constantly moves and the position also constantly moves, increasing steadily. So if it is increasing steadily, we can say that object moves. Yes, the object moves. It changes the position, right?

There's motion. And we can say that the object is moving with constant speed or constant. velocity. But in this case, since there is position here and it increases steadily, we can say that that's constant velocity. Next one, same as with the second graph, the line increases, but it is not steadily increasing.

As you can see here, the time changes. The position also changes with respect to time. However, the position increases slowly at the start and it moves faster at the second part of the graph. Meaning, there is an acceleration from a slow motion to a faster motion. And therefore, object is moving with constant acceleration.

So you can understand or you can actually interpret graphs, and you can formulate interpretations afterwards. By understanding first or by knowing first what are the x and y-axis, so that you can know what the lines mean. So aside from the position time graph, I have here the velocity time graph. Velocity symbolizes letter V. Time is letter V. 30 and velocity is in the y-axis, time is at the x-axis.

As you can see here, there's a green line over here at this part. Time changes but the velocity is not increasing nor decreasing. Therefore, we can say that the object is at rest because that's velocity.

Velocity is equal to the change in the displacement per unit time. There's no changes in the velocity, therefore there's no movement. The object is at rest.

The next one, as you can see here, time also changes. Velocity now is non-zero. Non-zero. So therefore, the object is not at rest, but it is in terms of constant velocity.

It moves through constant velocity. And therefore, The velocity here, I mean, the y component here is constant because the velocity is constant. And lastly, we have here the third graph.

So again, the time changes, but the velocity also changes. And if there's changes in velocity per unit time, there is an acceleration. object is moving with acceleration. So I hope by now you can understand these time gaps.

There are some exercises here. You can try to answer this. You can read first the content of the slide and then pause this video. After five seconds, I will try to answer this.

But again, in order for you to test your understanding of the lesson, you pause this video and then I'll count until five. then I'll answer the questions. So I hope by now you have your answers already. Then you pause this video.

Let's try to answer this. Given the following position time plots, so there's position time plots, answer the questions below. So first one, which pertains to an object with constant speed?

Again, we're talking about position time graph. Therefore, if there's a constant speed, the position must steadily increase. And as you can see in the four plots that we have, only letter B has a constant or a linear increase or changes in the position. And therefore, the answer is letter B. Okay, next one.

Which pertains to an object that reverses direction? What do we mean by that? Okay, so we can have a graph that in terms of position, it goes up. And then if it reverses direction, it goes down, moving nearer to its original position.

And actually, there's a graph pertaining to that, and that's letter A, right? Because as you can see, if this is the starting position, the time increases. But this part of the curve, it goes away to its original position.

But at this point, it reverses direction and maybe after some time, it goes back to its original position. Okay? As the time changes.

So, that's the answer. And lastly, which pertains to an object that starts slowly and then speeds up. So, the manifestation of an object that starts slowly, the increase of the first one is not that fast.

And then, after some time, it gets faster and faster. And actually, that pertains to letter D. Kasi mabagal siya sa umpisa, mataas yung pag-increase niya sa dulog.

So I hope nakuha ninyo yung lamang sagot. Okay? Next. There are also questions here.

Again, you can try to answer this. You can pause this video. And after five seconds, I'll try to answer. So I hope by now you have your answers with you.

This plot is again a position time graph. And the questions are presented here. In which of the labeled points is the velocity of an object, for instance, 0, constant in positive, constant in negative, increasing in magnitude, and decreasing in magnitude?

So here are the answers. Why is that? First one, the velocity of an object is 0 at point 4. Because as you can see here, there is no change in the position. At this point, there's no change in the position. Therefore, no velocity is present here.

There's zero velocity here at point 4. Because if you noticed, the line was flat. Its position did not change at that particular point. Therefore, there's zero velocity.

Okay? Next one. Sa constant and positive naman, bakit kaya itong si 1?

Kasi, kumapansin mo, at this point 1, linear yung pag-increase niya, therefore, constant increase in terms of velocity, and positive siya, kasi pataas yung kanyang movement. Therefore, point 1 is the point wherein the velocity is constant and positive. Next one, ano naman daw yung point na constant and negative? Kitang-kita naman, na very linear tong sa 0.5 na to.

Okay? And bakit siya negative? Kasi instead, kasi if you are moving away from your position, that's positive. But if you are going back to where you've started, at least at this point or at the origin, it's negative.

Pababa ka kasi. Okay? So, Constant and negative is 0.5. Next, increasing in magnitude.

What happens if the velocity is increasing in magnitude? If you remember earlier, in the position time graph that we have, when it became, here, let's go back. In the position time plot, right?

The one that is not linear but curved. may possibility of an acceleration. And that's because nag-increase or nag-decrease yung magnitude ng velocity. So dito, increasing in magnitude yung sa 0.2, kasi tinignan mo, hindi siya linear.

And talagang mataas yung slope. And therefore, kung mataas ang slope, sa maikling panahon, sa 2 to 4 minutes, mataas ang increase or pagbabago niya sa position. Therefore, increasing in magnitude.

At ano naman yung area na decreasing in magnitude? Kung napansin mo naman, after niyang tumaas ng very steady and very high, dito sa point 3, bumagal siya. At a particular time, ang bagal ng pagbago ng position until mag-zero yung velocity sa point 4. Therefore, sinin nagdi-decrease in magnitude dun sa point 3 nagsimula. Okay?

So I hope at this point, ang skill na meron tayo is marunong na tayong mag-interpret ng mga plots. So, you can also try to answer this. At which point does the object have the highest displacement?

Okay? So, displacement is again final minus the starting point. I'll give you three seconds.

The answer is letter B. Kasi dito sa point na to, malayo siya doon sa original position niya. Okay? Siya yung may pinakamala yung pwesto sa kanya original position. So the answer is letter B.

Next, at which point is the object at rest? Hindi nagbago yung posisyon? Saan kaya yun?

Kitang-kita natin, ano? Pwede siyang... Sige, I'll give you pala 3 seconds to answer. Kitang-kita natin na hindi siya gumalaw yung posisyon saan?

Sa point E. No? Hindi gumalaw siya. nagplatu yung position.

And at the same time, hindi lang siya masyadong kita, pero pwede rin nating sabihin na nagplatu din siya dito sa point B. May area na kung saan nagplatu yung curve. Same as true with D. And therefore, may pagkakataon din sa B at sa D ay nagrest yung object. But the best answer here is letter E.

Next, at which point is the object fastest? Ibig sabihin, Saan siya mabilis nagbago ng position? I'll give you three seconds.

The answer is letter C. Kasi kung nakita mo dito, ang grabe yung in-increase niya ng position. Ay, in-increase, sorry. Changes niya in position. From a positive position to a negative position.

Sir, ano yung ibig sabihin ng positive saka negative position na yan? Pwede nating sabihin kung ganyan siya. Positive siya kapag going north. Negative siya if going south. Pwedeng ganun ang interpretation natin dyan.

Positive siya if going east. Negative siya if going west. Okay? For example, dito sa B, nandito siya sa may north. Tapos umalis siya dun sa north, papuntang south naman.

Okay? Kaya managahal ng positive or negative positions. Buhabalik din siya para ngayon.

Okay? So hopefully, naintindihan. ang papag-interpret ng mga plots. Next, acceleration. How do we define acceleration earlier?

That's the change in velocity per unit time. At ang velocity, may dalawang components yan. Nandyan ang speed, pero mayroon ding direction. So, acceleration can mean that there's a change in speed or a change in direction or a change in both. Okay?

There's also an acceleration if the... direction of the speeding up is also in line with the direction of the velocity. As you can see here in this figure, the car is moving here, so the velocity is moving to the east, going to the east, and the acceleration, the changes that you are trying to have, is also going to the east.

So if you're... Acceleration is in line with the direction of the velocity. Therefore, the car will speed up. Okay? So, it will be fast.

But if the case is different. For example, the car will go to this side. But you pressed the brake. So, therefore, there was friction.

The impact of friction increased. So, now, the acceleration will go to this side. So if that's the case, babagal ngayon yung Because velocity and acceleration have different directions.

But if it accelerates rather at an angle to velocity, for example, your velocity is here, and your acceleration is going here, the instance can be made in a different direction. So, it can be like that. Okay?

So, that's acceleration. Velocity over time. Okay? So those are the parameters that can help us describe how objects move. Other types of motion include free fall.

Basically, when we say free fall, there's only vertical motion. Ibig sabihin ng vertical motion, ito lang. Taas baba lang.

motion na pwedeng ma-apply dyan. And usually, it goes down because of gravity. The gravitational pull of the Earth.

Okay? So, here, you have some facts about the free fall, free falling objects. The gravitational pull of the Earth on an object results in a falling motion, pababang motion. Kung mapapasin mo, no? If you, taw dito, allow a billiard ball, to fall freely.

If you notice where it started, it's a bit slow, but, um, people here, photographs will reveal that it's very fast. That it's very fast after some time. That's because gravitational acceleration. We have uh, speed in the drop of gravity down. And actually, on Earth, that is 9.8 meter per second squared.

yung pag-accelerate niya. Yung pagbulusok niya pababa. That's 9.8 meter per second squared.

The acceleration of an object varies with the distance of the object from the Earth's surface. Kaya ngayon, ginagawa natin constant. Na 9.8 meter per second squared, basta nandito sa Earth. Aside from that, the acceleration of an object does not vary with the mass of the object, at least at this point. Hindi siya...

hindi siya nakaka-apekto sa gravitational acceleration, and any falling body will experience air resistance slowing down its motion. Yung air resistance, ito yung parang pumipigil sa pagbagsak. Diba? Parang yung feather. Ang feather, kapag may buhabagsak na feather or balahibo, diba, mabagal yung kanyang paggalaw or pagbaba kasi there's an air resistance.

May pumipigil doon sa balahibo to go down easily. But in terms of free fall, We need to have assumptions so that we don't have a hard time. We must neglect air resistance. Okay?

We define now free fall as the constant acceleration of a body falling under the influence of Earth's gravitational attraction. It means that the movement is vertical. The movement is vertical. And the acceleration due to gravity is 9.8 meters per second squared. It's positive if it goes down because Okay.

Pabilis ng pabilis yung pagbuluso. Kaya positive. But if it goes up, it is negative kasi against ka sa gravity. So that's free fall.

Okay? Meron siyang relative, which is projectile motion. Or projectile motion. Ito, may involvement pa rin of gravity. However, this motion is characterized by simultaneous vertical things to gravity and horizontal movement.

because of the angle when you throw the ball. So, for example, you throw the ball, for instance. For example, you throw an object at this point, you place it at an angle, it has a trajectory, or it has a path that it runs. So, what is called a path taken by the projectile is its trajectory. But again, In terms of projectile motion, it is only influenced by gravity.

So talaga may vertical movement. And at the same time, because it is at an angle, may horizontal movement din siya. As you can see here, there is an independence of X or the horizontal movement in Y, the vertical movement. There are two. uh objects here one is a red ball the second one is a yellow colored ball but yeah the red ball was, what do you call it, was dropped in terms of free fall because, look, it's vertical.

It's just a vertical movement. Down. And then, the yellow ball was dropped at an angle. There's a projectile.

So, it's not just vertical down, but there's an angle. But if you notice, in the photographs, even if you say they have a different way of falling, At this particular time, they're both here. They're the same y-axis. At this time, they're still the same.

So, what does that mean? At any given time, both balls have the same y-position or y-axis and y-velocity despite having different x-positions and x-velocities. So, therefore, because the x and y are different, naman palang X and Y We can separate the computation of horizontal and vertical parts of a projectile. Because we said that a projectile is not just vertical like a free fall. It has vertical thanks to gravity and horizontal movement thanks to an angle when you throw an object.

In general science, we cannot complete that. But that's it. Ang projectile may vertical sa horizontal components. Next, we have uniform circular motion. Uniform circular motion, from the name itself, it is the motion along a circular path with constant speed.

Constant yung kanyang speed. Anong pinagkaiba? Bakit kaya ang velocity is always changing?

It's because dahil bilog siya, Kahit nasabihin mong constant speed siya, kailangan niya mag-change ng direksyon. Kasi, for example, ito yung bola, kapag hindi siya nag-change ng direksyon, gaganyan siya. Hindi siya magiging circular.

So, therefore, kailangan niya magbago ng direksyon. At sa pagbago niya ng direksyon, maapektuhan ang velocity, being a vector quantity, and acceleration, na kailangan din ng direksyon. Okay? So, Velocity and acceleration both have constant magnitudes kasi nga same yung velocity, constant, I'm sorry, constant rather yung speed. Pinagkakaiba is may pagbabago sa directions.

So that's uniform circular motion. And dito sa uniform circular motion, mayroon tayong tinatawag na centripetal force and centripetal acceleration. Centripetal force is a center-seeking force.

Ito yung dahilan kung bakit nagsistay sa bilog yung objects. So, for example, yung car na umiikot pa bilog, may tendency naman siya to go out of the circular path. But because of centripetal force that goes, papunta sa center, it keeps the object moving along a circular path.

At dahil, nasa circular path siya, may pagbabago sa direction every time na umiikot siya ng bilog. At dahil may pagbabago sa direction, masasabi natin that there is an acceleration. Okay? So there is an acceleration.

So there are examples of centripetal forces. So later on, we will discuss this. Yung tension, gravity. and friction.

Why did they become examples of centripetal forces? But also, you can search, you can do research, why are these examples of centripetal forces? Last slide, for this part of the masterclass, we have torque. Torque basically is a twisting force.

Okay? And because it's a twisting force, It allows rotation. But basically, for us to understand torque, alam naman natin siguro na may pinto. This is an example of a door. Torque is situated here sa may hinge.

Alam nyo yung hinge yung sa pinto. Diba sa pagitan ng pinto, tapos yung frame ng pinto, meron niyang parang, yan, yung nagkakos ng movement. Okay? Parang mga turnilyo.

Diba may mga turnilyo sa part na yan. Tapos, You won't see a door that the doorknob is near this region or this twisting area. Lagi ang doorknob nandun sa kabilang dulo. Because, di ba, kapag nagbubukas at sara tayo ng pinto, saan tayo nag-a-apply ng force?

Nag-a-apply tayo ng force doon sa doorknob. So, ano sinasabi ng torque? Para daw ma-ensure na mas mataas yung twist, kailangan yung object na pinag-a-applyan mo ng force ay malayo sa torque or malayo sa hinge. Okay?

Dapat may distance. Atatawag dun sa distance na yun ay lever arm. Okay?

Lever arm. So the higher or the longer the lever arm at may ina-apply kang force, mas mataas yung torque and therefore, mas mabilis or mas madaling it twists yung pinto. Kaya nabubukas at saran mo siya. Kasi kapag dito mo nilagay yung doorknob, Pag dito mo nilagay yung doorknob, dahil napakalapit niya doon sa hinge, ang liit nung lever arm. Ang liit nung lever arm mo.

Or ang liit nung distance between the hinge and doon sa doorknob, which, again, doon tayo nag-a-apply ng force. And therefore, mababa to, mababa din ang torque. Therefore, maliit lang yung twisting force.

So, kailangan mo mag-exert ng sobrang taas na force para lang ma-twist mo yung... So, that's the reason why the door knob is far from the hinge. Or, it's like there are screws. That's because, if it's far, there's only a little force that you need to exert in order for you to twist those hinges or those screws. Okay?

Question so far? So if you have questions, please write it down sa mga notes ninyo. Or you can also write your questions sa ating comment section dito sa video na ito. And we will try to answer those ating next na face-to-face masterclass. So I hope you've learned something about kinematics.

Nakita natin that there are different parameters to describe how objects move. There are also different types of motion. Okay?

So in the next masterclass, we'll focus on the remaining two branches of mechanics. We'll discuss dynamics and statics. Thank you so much for watching this video.

Goodbye. See you next time.

Transcript for:Introduction to Mechanics

Transcript for:
Introduction to Mechanics