Understanding Dynamics: Moments and Equilibrium

Hello friends, Jai Nepal! Today we are here with you with the Dynamics Go! We are here with important topics. In today's video, we are going to talk about what is called Moment. We have studied Momentum, but what is the word that sounds similar to Moment? Moment, where students get confused. So, there is Moment, Torque and Equilibrium. Then we have translational equilibrium and rotational equilibrium. Then we have solid friction, coefficient of friction, angle of friction and angle of repulse. So without further ado, we will start our class with science. So we will start with the moment. Now look at the force. We have applied force. In all the topics we have studied in dynamics, we have applied force. But force generates only translational motion. We read Newton's first law, second law, third law, momentum law. We read that horizontal motion is the same as linear motion. the If someone is traveling in a horizontal plane, we call it translational motion. Like we have a problem with our heart and cart, we have a problem with our lift system. Where is the lift coming from? It is coming down. All these are translational motion. Linear motion. Horizontal motion. Now we will talk about how force generates rotational motion. For example, What we can do is, if we fix this dot pen at any point in the axis, what happens if we apply force like this? If we apply force here, it is not going straight. It is moving. This generates rotational effect. Now, let's start rotating the rotation motion. Rotational motion is the moment of a force. that any object, moment or torque, let me read both of them together, moment of a force or torque, what do we call moment or torque? Right? This effect of force is applied in rotational motion. Rotational motion means rotation in 360 degree motion. Let us make a wheel. If we fix the axis of the wheel at this point, the force applied to the wheel will rotate the wheel. Now, we will learn the formula of the moment. The product of the force and the momentum are or the product of the force and perpendicular distance from the axis of rotation. If we imagine that this is our roof, imagine that this is your roof. Door is the rotation of the door from which the door is opened and closed. just like your copy wire If you fix this, we will open the door and close the door. This point will be fixed and axis of rotation will be here. And then we will open and close the door. Now look at the moment. I am applying force here. Axis of rotation is here. This is connected axis of rotation. From here, what is the perpendicular distance? With respect to the force, what is the perpendicular distance? If we do product of both, we call it moment. like him and so on. For example, here we are applying force into perpendicular distance. For this, we call force into perpendicular distance as moment. Moment is represented by tau. The force into perpendicular distance is called as Moment. If we want a clear concept of moment, it is a door. If I force here, it will be easy to close or open the door. But if I reduce the distance, I will have to force here. If you are going to take a new car, you should close the handle bar or open the door. Push towards the corner and push the bar to the end. We need to apply a little force. But if you are going at half distance, you need to apply a lot of force. If I apply a lot of force at the axis of rotation, I need to apply a lot of force. I have put force here, I can bend the copy easily. Or not bend, but keep it straight. We are talking about the door. Perpendicular distance should always be straight line. So, this is done. This is done. This is done. If I think this is a hole. This is the axis of rotation. Now if I want to push, I need to apply a little force in the perpendicular distance. If I want to push in the middle, I need to apply a little force. Similarly, I need to apply a lot of force as I go closer to the axis of rotation of the turning point. And this is an experiment that we can do at home. So, look at here. If we look at the wheel of a bicycle, it is a radius. If we apply a perpendicular force, it will turn. So, the moment and torque are the forces of the motion. Whenever we apply the force, the body starts rotating about its axis. So, look at here. This is a door. This is a door. Where is the axis of rotation? It is here. The moment is very clear concept. Let's do physical interpretation. What is this? This is a door. What is this? This is a door. What is this? This is a door. What is this? This is a door. What is this? This is a door. What is this? This is a door. What is this? F R1 mono We are applying F1. Now, if someone comes and forces at this point, applying F2, what is the having distance? Having distance is R2. What is the distance? R2. Someone may wish to apply force at F3, but what is the perpendicular distance here? What is the perpendicular distance in respect to force? Here also, if we search for the perpendicular distance in respect to force, me. This is also perpendicular. Now, what we have to do is to close the hole. Moment is constant. Moment means turning effect. Turning effect is constant. First, what is the person doing? F1 and R1. What is the first moment? F1, R1. Force into perpendicular distance. After this moment, the hole is opening. Now, someone has to do the moment first. Thank you for watching. Now, let's keep the moment same. Now, if you have a distance of R1, it is F1 condition. In F2 condition, the distance is decreasing. The distance is decreasing from the axis of rotation. R1 is here and R2 is here. The time when the distance is decreasing, you have to increase the force here. What does moment mean? If we keep the moment constant again, F2 is equal to R2 and F3 is equal to R3. But what we observe is that if R1 is decreasing from R2, where moment is constant and radius is R1, R1 is very long and R2 is shorter than that. Because the axis of rotation of R1 is very long. R2 is short distance. R3 is short distance. If we are reducing the distance between R1, R2 and R3, we need to increase the force. Because after all, what we need to do is to close the door. We need to keep the moment constant. We can experiment in our own house. Push the handlebar towards the corner and the force will be released. Push in the middle and then we have to apply more force to the handlebar to release the force. If you push the handlebar towards the axis of rotation, We need to apply a lot of force and our hands are also hurting. So what do mechanics do to open the nut bolt? If there is a wheel or nut bolt, mechanics don't use small wrench. They use a big wrench. So that the bigger the wrench, the more force is required. axis of rotation The bigger the range, the more momentum we can produce. Because momentum is a force into perpendicular distance. The more the distance is increased, the more the momentum is proportional to the distance. The more the distance, the more the mechanics are using the force to increase the distance. If you are using a small wrench, you can easily open a small knot ball. But if you are using a big long wrench, it will be very easy to open a knot ball. If you are using force constant, you can increase the radius of the knot ball. If you are using perpendicular distance, you can increase the moment turning effect. to you I'm rookie boy oh Moment. Momentum means the quantity of motion contained in a body. Here we have to keep the difference between momentum and moment. Momentum means mass into velocity. Moment means force into perpendicular distance. This is actually scalar. This is torque. Torque is also a moment. But this is a vector. This is a vector. Torque is a vector and in a vector form, So tau equal to R into F. Both are the same thing. The torque is the vector quantity. Just like a screw. screw is like this now we will see the path if you have tightened the screw what we have to do is or if we have to do any knot bolt How to rotate the screw? Rotate from the center. It can be a little difficult to understand. So what we do is, take an hexagonal or octagonal knot bolt. Now you will need a ring like this. What happened? You have a ring like this. Take it. What we have to do with this knot bolt is, If we tighten the knot bolt in this direction, What does it mean? If we tighten the knot bolt in this direction, So, from this point we are turning. So, what is this? R. And from here we are applying force. So, here we are applying vector quantity. Force is also vector quantity. distance is also the same. This is the product of two vectors. Especially in the Prajurita book, the force is in front. I am confused because I am in front. So I will put it in the back. The direction should be the same. If we apply force like this, you can think about it. This is the radius. If we apply force from here, How far can we turn? In clockwise direction What is clockwise direction? If we tighten it like this If you want to take the knot out from the inside, you have to reverse it in the anti-clockwise direction. But if you don't have a knot boat, you have a dot pen, you have a base of the dot pen, you have to turn it in this direction. If we rotate it in this direction, it will close. It will go inside. This is the vector quantity. The direction of this is the right hand thumb rule. If we rotate it like this, like you do top plane like you know you don't like a man whammy Let's consider one as radius and the other as force. The knot bolt goes in this finger. This is the inside and this is the force. The direction of torque is determined by the right hand thumb rule. But torque is also a moment. Torque is also a moment that generates the rotational effect. The formula will remain the same. Just remember that moment is scalar, torque is vector. Now we will go clockwise and anticlockwise. Now the simple thing is that we take one out. If we have to turn at this point, we go clockwise and anticlockwise moment. clockwise and anticlockwise moment. So now see, where does the clock go? Where does the clock go? 12, 3, 6, 9. If it goes from 12 to 3, then the clock goes from 1 to 3, then 3 to 6, okay? So what we want is this clockwise boil. 1 to 3 means 1, 2, 3. 3 to 6 means 4, 5, 6. So if our, right? What is this? The distance is R, okay? Ready, I'm important. If we are putting force in this direction, it will rotate in clockwise direction. But if we put force in this direction, it will rotate in anti-clockwise direction. This is anti-clockwise and clockwise movement. If we don't want it from the corner. Now what happens is that if we look at something from the middle, If we rotate from the center, what will happen? Now, we will keep axis of rotation from the center. And then what we will do? Here we will apply a force Apply force here And here we will apply force here Now we have F1 Distance from here is also from axis of rotation Distance from here is R1 Distance from here is R2 And for force it is F2 Now what is the principle of moment What is the principle of moment When we are talking about this the army. Axis of rotation is not in the end of any bar. It is between two ends. Principal of moment is clockwise moment is anti-clockwise moment. moment. It means, one moment, which is the total sum of the clockwise moment. Whatever the clockwise moment is, whatever the moment is in the clockwise direction, the sum of all of them is equal to the sum of all the moments in the anticlockwise direction. That is called as what? Principle of moment. What is principle of moment? clockwise moment is equal to the total sum of the vector sum of the vector sum of the clockwise moment is equal to the vector sum of the Anti-clockwise moment. Clockwise moment. Now clockwise. Which force rotates clockwise? Does this side force rotate clockwise? Or does this side? Now see. Where does the clock rotate? 12 to 3. In this direction. What does this force do? It rotates this bar. Where does it rotate? In clockwise direction. From here. Okay. From here. But what does this force do? This is the direction of the clock. If we force the clock, it will rotate in the opposite direction. If you have a clock, look at the clock. It will rotate in the opposite direction. If you force the clock, it will rotate in the opposite direction. It is an anti-clockwise direction. Similarly, what we do here is, Clockwise moment means how much force is applied? F2 and perpendicular distance is equal to R2. anti-clockwise is F1 force into F1 and R1 now let's assume that someone has loaded a car a year ago load is also a weight of Mg We don't understand the difference between F1 and F2. F3 is the force of weight and mass of the body. F3 is the force of the axis of rotation. Now, let's see how much force we are applying to this body. Therefore, having distance R4. Now, we have written F2 in clockwise direction. Now, another moment is also applied in clockwise direction. F4. This force is also applied in clockwise direction. So, we write F4 R4. So, we have written one in anti-clockwise and the other one is F3 plus F3R3. So, we can apply different forces in the same bar in two or more than two points. Like this. We can apply force here, of moment. Okay? So, this is how we can express something. Okay? Now, another topic is talk due to a couple. What does couple mean? What is a couple in our normal language? Right? What is a couple? It means two. If we apply force in two places, if we apply force in two places, the body will rotate. It comes in rotational motion. It comes in rotational motion. It comes in rotational motion. What we have to learn before this is that it is the same. It is the same. What do we call it? If we are applying force in same direction in same point of axis of rotation, then we have like parallel force. At this time, the body can rotate or not. If there is a difference in force, then there is rotation. Suppose, he applied a little force and she applied a lot of force. This means that there can be rotation. But if both are equal, then there is no rotation. Suppose, this is the copy. And if we apply the same force in both the ends, then this rotation will not happen. Let's talk about rotation. We can say that there are like and parallel forces. But if we take the same point of rotation and apply one force upwards and another force downwards. Now what will happen is, we will not place the top on top, we will place it on top. We will place the top on the outside. We will place it like this. And what will we do with this? We will place it on the outside as well. What does this mean? If this is there, I will lift it from the top on one side. We will give a name to this end. We will give a name to this end. If we put force on A, it will be lifted from the top. If we put force on B, it will be lifted from the bottom. The force from the bottom is pure rotational motion. Here, torque is generated. Because of torque generated by two couple of moments. Here, torque is generated. torque due to the couple. This is not like, it is parallel but it is unlike. Because this is in upward direction and this is in downward direction. Direction is different and unlike moment. This is like moment. Like and parallel moment. Because both the force are in same direction. And both are parallel with each other. I don't know, I don't know. This also has two forces parallel. But this is like and this is unlike. Because the direction is different. Now torque due to the couple. Due to the couple, the force applied at two points generates torque. It generates a rotational motion. What does total torque mean? Here we have a condition total torque which is a vector quantity. If we give F1 here and R1 distance from the point of axis of rotation and R2 distance from the point of axis of rotation. F2 is F2. Okay. So, what have we studied? What have we studied about torque? What have we studied? We have studied vector product. Okay. That is perpendicular distance into force. Right. So, what we are doing here is. What we are doing here is. Perpendicular distance is R1 times F1 plus total. Total is here. Total is here. Clockwise and anticlockwise is here. This is clockwise and this is clockwise. This is because of two forces. Which direction is the body moving in? If you are applying force here, then this is here. If the force is applied, the body will rotate in the same direction. If the force is applied, the body will rotate in the same direction. What does this mean? The rotational effect of this is the same as the one of the two. If you move in this direction, it will be in anti-clockwise direction. If you move in the clockwise direction, it will be in the unipo- direction. This bar is in anti-clockwise direction. It rotates the body in this direction. This force rotates in this direction. This is opposite of 1. So, when it is opposite, it can be minus. But, if we do it in upward direction from here and downward direction from here, what is the total resultant? Two. Now, its speed increases. If we apply force from the same side, what is its speed? It is less. But, if we apply force from both sides, the reason for this is that its rotational effect, rotational speed, rotational velocity increases. one. If we apply force from both sides, the rotational effect increases. So, R1 plus F1 equals R2 plus R1 into F. So, what is this? Rotational torque duet couple. If we apply force from here and move it from the top, what happens? Or, for example, if we move it from the top and from the bottom, if we move it at a speed like this, what happens if we move it like this? The speed increases. But, if we move it like this, what happens? What happens if we increase the speed? Rotational thing is with us. We are going to show you how to make a cycle. What you need to do is to move the tyre from both sides. This will increase the speed of the wheel. Because the wheel will move both sides. So we are joining the forces due to torque. If we rotate the force clockwise, we get this. But if you put the tyre on one side and the other side is on the other side, then there is no speed. There is a minus and a plus. torque due to couple. So overall if we read this, what we read till now? Moment, moment means force into perpendicular distance, torque is also there but in vector quantity. Then what we read? Clockwise and anticlockwise moment. Then what we read? Principal up moment, then torque due to the couple. Now we will study translational equilibrium. How long can we say anything in equilibrium? Either it is totally restful. We are learning about the Translational Equilibrium. The body should be in rest. uniform motion. What does translational equilibrium mean? Translational equilibrium Equilibrium means, if the external force is equal to zero, then the vector sum of the force is zero. I am holding two hands and my left hand is moving this way and my right hand is moving this way. Total force is there. Total vector sum of the force is zero. If the vector sum of the force is zero, then we can write the vector sum of the force is equal to 0. We can call it translational equilibrium. or the equilibrium of any body, that is called net force. We can call it as vector sum of force or resultant force. net force bonus also total force bonus also again Tara vector can only force the already vector quantities are the total force ready to Matthew the G a career total force yeah the total in resultant force here the zero so So, the vector sum of force is zero. It is not an extra force or an external force. So, the body is in translational equilibrium. If the car is in uniform motion, the vector sum of the force should be zero. What does force mean? Mass into acceleration equals zero. Master Zero cannot exist except for the spirit, the soul. So, acceleration should be zero. So, if any body has zero acceleration, the final velocity of any body is the same as the initial velocity. So, zero by t is zero. Meaning, if any body is in uniform motion, what is that? So, what is that? Translational Equilibrium Just like a car, you are travelling in your own car or bike If we are travelling in constant speed, our car will neither go forward nor backward It is in equilibrium state. We can keep a glass of water in the car. It will not move for long. The speed will be constant. The velocity will be uniform. The velocity will be uniform. The same velocity. That will keep our body in equilibrium. Or the other thing is rest. Translational equilibrium means net force is 0 Net force is 0 Vector sum of force is 0 Resultant force is 0 Similarly, let's come to rotational equilibrium Rotational equilibrium means Rotation is there We applied force on this top We applied force on this top This is actually torque We applied torque on this top So this is the total. If the total torque is zero, the resultant torque is zero, then this body is in rotational equilibrium. If this body is in totally in rest or in uniform motion, Because we have learned the formula of torque as well. Perpendicular distance into force. So, how long will the net torque be zero? The radius cannot be zero. Because this is a rotational body and the radius is also same. So, force must be zero. Force is mass into acceleration. Mass is never zero. R is never zero. Similarly, acceleration must be zero. So, if the body is in rest here, and that's where we end up. Uniform motion is called rotational equilibrium. So, both must be equal. To have something in equilibrium, resultant must be equal to net vector sum of force. So, it must be zero. For translation, for rotational, vector sum of the torque must be zero. Now, we will come to solid friction. Now we will talk about solid friction. Solid friction is the friction applied to the solid body. The modern concept of solid friction is that if two surfaces are together, it is due to friction. Like here, it's not sliding anymore. Due to the friction, the surface is not sliding due to friction. If we talk about solid friction, if there is an object, the object is too big, right? If there is an object, if we, if this person, If this person is moving this force towards here, then the force will go towards here. Friction is in opposite direction of force What do you mean by frictional force? This is also a force Each and every action has opposite reaction If we denote this force here Friction is in opposite direction of force This is called frictional force We denote this by EF here What does frictional force mean? boy Which opposes the force which opposes the direction of the which opposes the motion Yes, which opposes the motion is called as friction force. Okay, the motion Motion like opposed got so roxa foot well here countable football kina rusa due to the friction between the surface and the Football got even a brick like a busy guy. Do you know could or a cha due to the friction between the tires and the road? Yes, I mean, I'm more I mean a socket. Oh Why? We are able to move. Why? Due to the friction. We are stable. If there is no friction, we can move on. Friction force is always in opposite direction of the motion. The direction of motion is in opposite direction. This is friction. Solid friction is friction on solid object. If we look at the microscope, the atoms are arranged like this. As you can see, the finishing is very plain like tiles marble. But if you look at the inside, the surface is very rough in nano scale. So, it is very flexible. But if you zoom in and look at it in electron microscope, the surface is not that smooth. The finishing is not as good as the body. this was also a me coefficient of Friction, to see the coefficient of friction, we have to look at something. So, look here, we have to put it in this direction. We put it in the opposite direction. Or if we put it here, it will not make sense. We put it in this direction, frictional force. Now look, what does it look like from below? Weight. And what does the body do to it? Every action has weight. Equal and opposite reaction. Reaction. What is this person doing? What is this person doing to this object? What is he doing here? He is moving it. What is he doing here? He is moving it. What is he doing here? direction, frictional force goes in this direction, so frictional force goes in this direction. I have made it here. Now, the vector sum, the vector, according to the rule of the vector, parallelogram of vector if we make parallelogram resultant of this resultant of this If we make a complete parallelogram, will it go in the direction of the diagonal? Yes it will. So what we will do is, it will go in the direction of the diagonal. What is this? This goes in the direction of the diagonal. This means Frictional force and Reaction. Reaction is weight. Let's understand this. The more reaction, the more weight. The more weight, the more reaction. This is called resultant. We will consider this as resultant. This resultant makes the angle. we call it alpha. To find coefficient of friction, we have to do friction is directly proportional upon reaction. Friction is directly proportional upon reaction. What does it mean? There is a light object, a light body, a little weight, if there is a little weight, if there is a little reaction, it will be easy for me to move it from one place to another. But the more weight, The more happy your body is, The more heavy it is, the more it reacts. Heavy weight pushes the ground with heavy force. The more it pushes the ground, the more it pushes the ground. So friction, The more weight we have, the more these two molecules will be attached to each other. They are attached to each other, and the rough surfaces will be locked with each other. So, the more we have in something, the more atoms will be close to each other, interlocked. The rough surfaces of each other will be interlocked. So, that is why we are We need to apply force to move the object. It is easy to slide a 1 kg rock but it is difficult to slide a 1000 kg rock. Because 1000 kg rock is heavy and it requires a lot of force. The more force applied, the more the reaction is. Actually, the weight is more important. Here, the friction force is directly proportional to the weight of the body. But what we do without writing the weight is we write the reaction. Weight and reaction are the same thing. Horizontally, not on the inclined surface. We can make a lot of reactions. Especially, we can make the surface a little bit more plane. So, we don't depend on weight. Because we can make the surface smooth, we can grease it, we can oil it. We did reaction without weight line. The reaction of surface is based on the amount of friction. Now we will introduce constant which is the coefficient of friction. Mu is equal to F L by R. F L by R is the coefficient of friction. Frictional force upon reaction. is This is also a force. Both of them cancel each other. Now, what happens? Frictional force is here. Reaction is here. Resultant of both forces is diagonal. Now, if we want to calculate angle of friction, angle of friction is alpha. Now, let's do parallel. This is EFL and this is EFL. For a moment, this is 90 degree. Now, we will play with respect to alpha. tan alpha equal to perpendicular. So, this angle is perpendicular. perpendicular means F L and base is R. So, we will play with tan alpha equal to F L by R. F e l by r is mu. So this is angle of friction. If you know this angle of body, tan alpha is coefficient. center of friction coefficient of friction negar no so honey I mean yeah angle but upon a Nikola so so over psychic is a angle of repose angle of repose matlab kepo yo que ponepone inclined body ma ponepone inclined surface ma incline surface media the cunei body so money yeah say it's the egg dumb minimum angles a homily gurnu porio minimum angle katy unipoli theta where the body starts sliding. Like this body. Now see, if we slide, we start to incline the body slightly. This is called angle of repose. The minimum angle of an inclined surface with the horizontal at which the body starts sliding. of the plane surface with respect to the horizon at which the body starts sliding that is called as angle of repose. 90 degree angle is mg sine theta What is behind? Body is coming in this direction Frictional force is coming in this direction Frictional force is coming in this direction Body is coming down Frictional force is opposite Reaction is done by surface What is above surface? Friction depends on surface reaction This surface is very hard to draw. But if we incline it, it will be less difficult. Because it is in inclined form. If we do this here, If we do this here, What can we write here as alpha equal to? What can we write as EFEL by? EFEL by R. What is EFEL here? Newton's third law. Every action has equal and opposite reaction. What does EFEL mean? This is equal to its opposite direction. Because it is in this direction. F reaction has equal and opposite reaction. EFL means MG sin theta. What is here? R is reaction. Reaction is above. We compare with the bottom. MZ What is mg? mg cos theta. mg goes to alpha equal to tan theta. Here also if we get coefficient, if we get coefficient, here if we get, this is not alpha, this is mu. If we want to calculate the coefficient of friction, we can calculate the minimum angle of repose of any body on the inclined surface. We can calculate the coefficient of friction by writing tan and angle of repose theta. That's all for today. We will meet you in the next chapter. Thank you for watching.

Hello friends, Jai Nepal! Today we are here with you with the Dynamics Go! We are here with important topics.

In today's video, we are going to talk about what is called Moment. We have studied Momentum, but what is the word that sounds similar to Moment? Moment, where students get confused. So, there is Moment, Torque and Equilibrium. Then we have translational equilibrium and rotational equilibrium.

Then we have solid friction, coefficient of friction, angle of friction and angle of repulse. So without further ado, we will start our class with science. So we will start with the moment. Now look at the force.

We have applied force. In all the topics we have studied in dynamics, we have applied force. But force generates only translational motion. We read Newton's first law, second law, third law, momentum law.

We read that horizontal motion is the same as linear motion. the If someone is traveling in a horizontal plane, we call it translational motion. Like we have a problem with our heart and cart, we have a problem with our lift system. Where is the lift coming from? It is coming down.

All these are translational motion. Linear motion. Horizontal motion.

Now we will talk about how force generates rotational motion. For example, What we can do is, if we fix this dot pen at any point in the axis, what happens if we apply force like this? If we apply force here, it is not going straight. It is moving. This generates rotational effect.

Now, let's start rotating the rotation motion. Rotational motion is the moment of a force. that any object, moment or torque, let me read both of them together, moment of a force or torque, what do we call moment or torque?

Right? This effect of force is applied in rotational motion. Rotational motion means rotation in 360 degree motion.

Let us make a wheel. If we fix the axis of the wheel at this point, the force applied to the wheel will rotate the wheel. Now, we will learn the formula of the moment.

The product of the force and the momentum are or the product of the force and perpendicular distance from the axis of rotation. If we imagine that this is our roof, imagine that this is your roof. Door is the rotation of the door from which the door is opened and closed. just like your copy wire If you fix this, we will open the door and close the door. This point will be fixed and axis of rotation will be here.

And then we will open and close the door. Now look at the moment. I am applying force here. Axis of rotation is here. This is connected axis of rotation.

From here, what is the perpendicular distance? With respect to the force, what is the perpendicular distance? If we do product of both, we call it moment.

like him and so on. For example, here we are applying force into perpendicular distance. For this, we call force into perpendicular distance as moment.

Moment is represented by tau. The force into perpendicular distance is called as Moment. If we want a clear concept of moment, it is a door.

If I force here, it will be easy to close or open the door. But if I reduce the distance, I will have to force here. If you are going to take a new car, you should close the handle bar or open the door.

Push towards the corner and push the bar to the end. We need to apply a little force. But if you are going at half distance, you need to apply a lot of force. If I apply a lot of force at the axis of rotation, I need to apply a lot of force. I have put force here, I can bend the copy easily.

Or not bend, but keep it straight. We are talking about the door. Perpendicular distance should always be straight line. So, this is done. This is done.

This is done. If I think this is a hole. This is the axis of rotation.

Now if I want to push, I need to apply a little force in the perpendicular distance. If I want to push in the middle, I need to apply a little force. Similarly, I need to apply a lot of force as I go closer to the axis of rotation of the turning point. And this is an experiment that we can do at home.

So, look at here. If we look at the wheel of a bicycle, it is a radius. If we apply a perpendicular force, it will turn.

So, the moment and torque are the forces of the motion. Whenever we apply the force, the body starts rotating about its axis. So, look at here. This is a door.

This is a door. Where is the axis of rotation? It is here.

The moment is very clear concept. Let's do physical interpretation. What is this?

This is a door. What is this? This is a door.

What is this? This is a door. What is this?

This is a door. What is this? This is a door.

What is this? This is a door. What is this? F R1 mono We are applying F1.

Now, if someone comes and forces at this point, applying F2, what is the having distance? Having distance is R2. What is the distance?

R2. Someone may wish to apply force at F3, but what is the perpendicular distance here? What is the perpendicular distance in respect to force?

Here also, if we search for the perpendicular distance in respect to force, me. This is also perpendicular. Now, what we have to do is to close the hole. Moment is constant.

Moment means turning effect. Turning effect is constant. First, what is the person doing? F1 and R1. What is the first moment?

F1, R1. Force into perpendicular distance. After this moment, the hole is opening.

Now, someone has to do the moment first. Thank you for watching. Now, let's keep the moment same.

Now, if you have a distance of R1, it is F1 condition. In F2 condition, the distance is decreasing. The distance is decreasing from the axis of rotation. R1 is here and R2 is here.

The time when the distance is decreasing, you have to increase the force here. What does moment mean? If we keep the moment constant again, F2 is equal to R2 and F3 is equal to R3.

But what we observe is that if R1 is decreasing from R2, where moment is constant and radius is R1, R1 is very long and R2 is shorter than that. Because the axis of rotation of R1 is very long. R2 is short distance. R3 is short distance. If we are reducing the distance between R1, R2 and R3, we need to increase the force.

Because after all, what we need to do is to close the door. We need to keep the moment constant. We can experiment in our own house.

Push the handlebar towards the corner and the force will be released. Push in the middle and then we have to apply more force to the handlebar to release the force. If you push the handlebar towards the axis of rotation, We need to apply a lot of force and our hands are also hurting. So what do mechanics do to open the nut bolt? If there is a wheel or nut bolt, mechanics don't use small wrench.

They use a big wrench. So that the bigger the wrench, the more force is required. axis of rotation The bigger the range, the more momentum we can produce.

Because momentum is a force into perpendicular distance. The more the distance is increased, the more the momentum is proportional to the distance. The more the distance, the more the mechanics are using the force to increase the distance.

If you are using a small wrench, you can easily open a small knot ball. But if you are using a big long wrench, it will be very easy to open a knot ball. If you are using force constant, you can increase the radius of the knot ball.

If you are using perpendicular distance, you can increase the moment turning effect. to you I'm rookie boy oh Moment. Momentum means the quantity of motion contained in a body.

Here we have to keep the difference between momentum and moment. Momentum means mass into velocity. Moment means force into perpendicular distance. This is actually scalar.

This is torque. Torque is also a moment. But this is a vector.

This is a vector. Torque is a vector and in a vector form, So tau equal to R into F. Both are the same thing.

The torque is the vector quantity. Just like a screw. screw is like this now we will see the path if you have tightened the screw what we have to do is or if we have to do any knot bolt How to rotate the screw? Rotate from the center. It can be a little difficult to understand.

So what we do is, take an hexagonal or octagonal knot bolt. Now you will need a ring like this. What happened?

You have a ring like this. Take it. What we have to do with this knot bolt is, If we tighten the knot bolt in this direction, What does it mean? If we tighten the knot bolt in this direction, So, from this point we are turning.

So, what is this? R. And from here we are applying force.

So, here we are applying vector quantity. Force is also vector quantity. distance is also the same.

This is the product of two vectors. Especially in the Prajurita book, the force is in front. I am confused because I am in front. So I will put it in the back. The direction should be the same.

If we apply force like this, you can think about it. This is the radius. If we apply force from here, How far can we turn? In clockwise direction What is clockwise direction? If we tighten it like this If you want to take the knot out from the inside, you have to reverse it in the anti-clockwise direction.

But if you don't have a knot boat, you have a dot pen, you have a base of the dot pen, you have to turn it in this direction. If we rotate it in this direction, it will close. It will go inside. This is the vector quantity. The direction of this is the right hand thumb rule.

If we rotate it like this, like you do top plane like you know you don't like a man whammy Let's consider one as radius and the other as force. The knot bolt goes in this finger. This is the inside and this is the force. The direction of torque is determined by the right hand thumb rule. But torque is also a moment.

Torque is also a moment that generates the rotational effect. The formula will remain the same. Just remember that moment is scalar, torque is vector. Now we will go clockwise and anticlockwise. Now the simple thing is that we take one out.

If we have to turn at this point, we go clockwise and anticlockwise moment. clockwise and anticlockwise moment. So now see, where does the clock go? Where does the clock go? 12, 3, 6, 9. If it goes from 12 to 3, then the clock goes from 1 to 3, then 3 to 6, okay?

So what we want is this clockwise boil. 1 to 3 means 1, 2, 3. 3 to 6 means 4, 5, 6. So if our, right? What is this? The distance is R, okay? Ready, I'm important.

If we are putting force in this direction, it will rotate in clockwise direction. But if we put force in this direction, it will rotate in anti-clockwise direction. This is anti-clockwise and clockwise movement. If we don't want it from the corner.

Now what happens is that if we look at something from the middle, If we rotate from the center, what will happen? Now, we will keep axis of rotation from the center. And then what we will do? Here we will apply a force Apply force here And here we will apply force here Now we have F1 Distance from here is also from axis of rotation Distance from here is R1 Distance from here is R2 And for force it is F2 Now what is the principle of moment What is the principle of moment When we are talking about this the army.

Axis of rotation is not in the end of any bar. It is between two ends. Principal of moment is clockwise moment is anti-clockwise moment. moment.

It means, one moment, which is the total sum of the clockwise moment. Whatever the clockwise moment is, whatever the moment is in the clockwise direction, the sum of all of them is equal to the sum of all the moments in the anticlockwise direction. That is called as what? Principle of moment.

What is principle of moment? clockwise moment is equal to the total sum of the vector sum of the vector sum of the clockwise moment is equal to the vector sum of the Anti-clockwise moment. Clockwise moment.

Now clockwise. Which force rotates clockwise? Does this side force rotate clockwise? Or does this side? Now see.

Where does the clock rotate? 12 to 3. In this direction. What does this force do? It rotates this bar.

Where does it rotate? In clockwise direction. From here.

Okay. From here. But what does this force do?

This is the direction of the clock. If we force the clock, it will rotate in the opposite direction. If you have a clock, look at the clock. It will rotate in the opposite direction.

If you force the clock, it will rotate in the opposite direction. It is an anti-clockwise direction. Similarly, what we do here is, Clockwise moment means how much force is applied?

F2 and perpendicular distance is equal to R2. anti-clockwise is F1 force into F1 and R1 now let's assume that someone has loaded a car a year ago load is also a weight of Mg We don't understand the difference between F1 and F2. F3 is the force of weight and mass of the body. F3 is the force of the axis of rotation.

Now, let's see how much force we are applying to this body. Therefore, having distance R4. Now, we have written F2 in clockwise direction.

Now, another moment is also applied in clockwise direction. F4. This force is also applied in clockwise direction. So, we write F4 R4. So, we have written one in anti-clockwise and the other one is F3 plus F3R3.

So, we can apply different forces in the same bar in two or more than two points. Like this. We can apply force here, of moment.

Okay? So, this is how we can express something. Okay?

Now, another topic is talk due to a couple. What does couple mean? What is a couple in our normal language? Right?

What is a couple? It means two. If we apply force in two places, if we apply force in two places, the body will rotate.

It comes in rotational motion. It comes in rotational motion. It comes in rotational motion.

What we have to learn before this is that it is the same. It is the same. What do we call it? If we are applying force in same direction in same point of axis of rotation, then we have like parallel force. At this time, the body can rotate or not.

If there is a difference in force, then there is rotation. Suppose, he applied a little force and she applied a lot of force. This means that there can be rotation. But if both are equal, then there is no rotation.

Suppose, this is the copy. And if we apply the same force in both the ends, then this rotation will not happen. Let's talk about rotation.

We can say that there are like and parallel forces. But if we take the same point of rotation and apply one force upwards and another force downwards. Now what will happen is, we will not place the top on top, we will place it on top. We will place the top on the outside. We will place it like this.

And what will we do with this? We will place it on the outside as well. What does this mean? If this is there, I will lift it from the top on one side.

We will give a name to this end. We will give a name to this end. If we put force on A, it will be lifted from the top.

If we put force on B, it will be lifted from the bottom. The force from the bottom is pure rotational motion. Here, torque is generated. Because of torque generated by two couple of moments. Here, torque is generated.

torque due to the couple. This is not like, it is parallel but it is unlike. Because this is in upward direction and this is in downward direction.

Direction is different and unlike moment. This is like moment. Like and parallel moment. Because both the force are in same direction.

And both are parallel with each other. I don't know, I don't know. This also has two forces parallel.

But this is like and this is unlike. Because the direction is different. Now torque due to the couple.

Due to the couple, the force applied at two points generates torque. It generates a rotational motion. What does total torque mean? Here we have a condition total torque which is a vector quantity. If we give F1 here and R1 distance from the point of axis of rotation and R2 distance from the point of axis of rotation.

F2 is F2. Okay. So, what have we studied? What have we studied about torque? What have we studied?

We have studied vector product. Okay. That is perpendicular distance into force. Right.

So, what we are doing here is. What we are doing here is. Perpendicular distance is R1 times F1 plus total.

Total is here. Total is here. Clockwise and anticlockwise is here. This is clockwise and this is clockwise. This is because of two forces.

Which direction is the body moving in? If you are applying force here, then this is here. If the force is applied, the body will rotate in the same direction. If the force is applied, the body will rotate in the same direction. What does this mean?

The rotational effect of this is the same as the one of the two. If you move in this direction, it will be in anti-clockwise direction. If you move in the clockwise direction, it will be in the unipo- direction.

This bar is in anti-clockwise direction. It rotates the body in this direction. This force rotates in this direction.

This is opposite of 1. So, when it is opposite, it can be minus. But, if we do it in upward direction from here and downward direction from here, what is the total resultant? Two.

Now, its speed increases. If we apply force from the same side, what is its speed? It is less. But, if we apply force from both sides, the reason for this is that its rotational effect, rotational speed, rotational velocity increases.

one. If we apply force from both sides, the rotational effect increases. So, R1 plus F1 equals R2 plus R1 into F.

So, what is this? Rotational torque duet couple. If we apply force from here and move it from the top, what happens?

Or, for example, if we move it from the top and from the bottom, if we move it at a speed like this, what happens if we move it like this? The speed increases. But, if we move it like this, what happens? What happens if we increase the speed?

Rotational thing is with us. We are going to show you how to make a cycle. What you need to do is to move the tyre from both sides. This will increase the speed of the wheel.

Because the wheel will move both sides. So we are joining the forces due to torque. If we rotate the force clockwise, we get this.

But if you put the tyre on one side and the other side is on the other side, then there is no speed. There is a minus and a plus. torque due to couple. So overall if we read this, what we read till now?

Moment, moment means force into perpendicular distance, torque is also there but in vector quantity. Then what we read? Clockwise and anticlockwise moment. Then what we read? Principal up moment, then torque due to the couple.

Now we will study translational equilibrium. How long can we say anything in equilibrium? Either it is totally restful.

We are learning about the Translational Equilibrium. The body should be in rest. uniform motion.

What does translational equilibrium mean? Translational equilibrium Equilibrium means, if the external force is equal to zero, then the vector sum of the force is zero. I am holding two hands and my left hand is moving this way and my right hand is moving this way. Total force is there.

Total vector sum of the force is zero. If the vector sum of the force is zero, then we can write the vector sum of the force is equal to 0. We can call it translational equilibrium. or the equilibrium of any body, that is called net force.

We can call it as vector sum of force or resultant force. net force bonus also total force bonus also again Tara vector can only force the already vector quantities are the total force ready to Matthew the G a career total force yeah the total in resultant force here the zero so So, the vector sum of force is zero. It is not an extra force or an external force. So, the body is in translational equilibrium. If the car is in uniform motion, the vector sum of the force should be zero.

What does force mean? Mass into acceleration equals zero. Master Zero cannot exist except for the spirit, the soul. So, acceleration should be zero. So, if any body has zero acceleration, the final velocity of any body is the same as the initial velocity.

So, zero by t is zero. Meaning, if any body is in uniform motion, what is that? So, what is that?

Translational Equilibrium Just like a car, you are travelling in your own car or bike If we are travelling in constant speed, our car will neither go forward nor backward It is in equilibrium state. We can keep a glass of water in the car. It will not move for long. The speed will be constant.

The velocity will be uniform. The velocity will be uniform. The same velocity. That will keep our body in equilibrium. Or the other thing is rest.

Translational equilibrium means net force is 0 Net force is 0 Vector sum of force is 0 Resultant force is 0 Similarly, let's come to rotational equilibrium Rotational equilibrium means Rotation is there We applied force on this top We applied force on this top This is actually torque We applied torque on this top So this is the total. If the total torque is zero, the resultant torque is zero, then this body is in rotational equilibrium. If this body is in totally in rest or in uniform motion, Because we have learned the formula of torque as well. Perpendicular distance into force. So, how long will the net torque be zero?

The radius cannot be zero. Because this is a rotational body and the radius is also same. So, force must be zero. Force is mass into acceleration.

Mass is never zero. R is never zero. Similarly, acceleration must be zero.

So, if the body is in rest here, and that's where we end up. Uniform motion is called rotational equilibrium. So, both must be equal. To have something in equilibrium, resultant must be equal to net vector sum of force.

So, it must be zero. For translation, for rotational, vector sum of the torque must be zero. Now, we will come to solid friction. Now we will talk about solid friction. Solid friction is the friction applied to the solid body.

The modern concept of solid friction is that if two surfaces are together, it is due to friction. Like here, it's not sliding anymore. Due to the friction, the surface is not sliding due to friction. If we talk about solid friction, if there is an object, the object is too big, right?

If there is an object, if we, if this person, If this person is moving this force towards here, then the force will go towards here. Friction is in opposite direction of force What do you mean by frictional force? This is also a force Each and every action has opposite reaction If we denote this force here Friction is in opposite direction of force This is called frictional force We denote this by EF here What does frictional force mean?

boy Which opposes the force which opposes the direction of the which opposes the motion Yes, which opposes the motion is called as friction force. Okay, the motion Motion like opposed got so roxa foot well here countable football kina rusa due to the friction between the surface and the Football got even a brick like a busy guy. Do you know could or a cha due to the friction between the tires and the road? Yes, I mean, I'm more I mean a socket.

Oh Why? We are able to move. Why? Due to the friction. We are stable.

If there is no friction, we can move on. Friction force is always in opposite direction of the motion. The direction of motion is in opposite direction. This is friction.

Solid friction is friction on solid object. If we look at the microscope, the atoms are arranged like this. As you can see, the finishing is very plain like tiles marble.

But if you look at the inside, the surface is very rough in nano scale. So, it is very flexible. But if you zoom in and look at it in electron microscope, the surface is not that smooth. The finishing is not as good as the body.

this was also a me coefficient of Friction, to see the coefficient of friction, we have to look at something. So, look here, we have to put it in this direction. We put it in the opposite direction.

Or if we put it here, it will not make sense. We put it in this direction, frictional force. Now look, what does it look like from below?

Weight. And what does the body do to it? Every action has weight.

Equal and opposite reaction. Reaction. What is this person doing? What is this person doing to this object? What is he doing here?

He is moving it. What is he doing here? He is moving it. What is he doing here?

direction, frictional force goes in this direction, so frictional force goes in this direction. I have made it here. Now, the vector sum, the vector, according to the rule of the vector, parallelogram of vector if we make parallelogram resultant of this resultant of this If we make a complete parallelogram, will it go in the direction of the diagonal?

Yes it will. So what we will do is, it will go in the direction of the diagonal. What is this?

This goes in the direction of the diagonal. This means Frictional force and Reaction. Reaction is weight.

Let's understand this. The more reaction, the more weight. The more weight, the more reaction.

This is called resultant. We will consider this as resultant. This resultant makes the angle.

we call it alpha. To find coefficient of friction, we have to do friction is directly proportional upon reaction. Friction is directly proportional upon reaction.

What does it mean? There is a light object, a light body, a little weight, if there is a little weight, if there is a little reaction, it will be easy for me to move it from one place to another. But the more weight, The more happy your body is, The more heavy it is, the more it reacts.

Heavy weight pushes the ground with heavy force. The more it pushes the ground, the more it pushes the ground. So friction, The more weight we have, the more these two molecules will be attached to each other.

They are attached to each other, and the rough surfaces will be locked with each other. So, the more we have in something, the more atoms will be close to each other, interlocked. The rough surfaces of each other will be interlocked.

So, that is why we are We need to apply force to move the object. It is easy to slide a 1 kg rock but it is difficult to slide a 1000 kg rock. Because 1000 kg rock is heavy and it requires a lot of force. The more force applied, the more the reaction is.

Actually, the weight is more important. Here, the friction force is directly proportional to the weight of the body. But what we do without writing the weight is we write the reaction. Weight and reaction are the same thing. Horizontally, not on the inclined surface.

We can make a lot of reactions. Especially, we can make the surface a little bit more plane. So, we don't depend on weight. Because we can make the surface smooth, we can grease it, we can oil it. We did reaction without weight line.

The reaction of surface is based on the amount of friction. Now we will introduce constant which is the coefficient of friction. Mu is equal to F L by R.

F L by R is the coefficient of friction. Frictional force upon reaction. is This is also a force. Both of them cancel each other. Now, what happens?

Frictional force is here. Reaction is here. Resultant of both forces is diagonal.

Now, if we want to calculate angle of friction, angle of friction is alpha. Now, let's do parallel. This is EFL and this is EFL. For a moment, this is 90 degree. Now, we will play with respect to alpha.

tan alpha equal to perpendicular. So, this angle is perpendicular. perpendicular means F L and base is R.

So, we will play with tan alpha equal to F L by R. F e l by r is mu. So this is angle of friction. If you know this angle of body, tan alpha is coefficient. center of friction coefficient of friction negar no so honey I mean yeah angle but upon a Nikola so so over psychic is a angle of repose angle of repose matlab kepo yo que ponepone inclined body ma ponepone inclined surface ma incline surface media the cunei body so money yeah say it's the egg dumb minimum angles a homily gurnu porio minimum angle katy unipoli theta where the body starts sliding.

Like this body. Now see, if we slide, we start to incline the body slightly. This is called angle of repose. The minimum angle of an inclined surface with the horizontal at which the body starts sliding. of the plane surface with respect to the horizon at which the body starts sliding that is called as angle of repose.

90 degree angle is mg sine theta What is behind? Body is coming in this direction Frictional force is coming in this direction Frictional force is coming in this direction Body is coming down Frictional force is opposite Reaction is done by surface What is above surface? Friction depends on surface reaction This surface is very hard to draw.

But if we incline it, it will be less difficult. Because it is in inclined form. If we do this here, If we do this here, What can we write here as alpha equal to?

What can we write as EFEL by? EFEL by R. What is EFEL here? Newton's third law.

Every action has equal and opposite reaction. What does EFEL mean? This is equal to its opposite direction. Because it is in this direction. F reaction has equal and opposite reaction.

EFL means MG sin theta. What is here? R is reaction. Reaction is above. We compare with the bottom.

MZ What is mg? mg cos theta. mg goes to alpha equal to tan theta. Here also if we get coefficient, if we get coefficient, here if we get, this is not alpha, this is mu.

If we want to calculate the coefficient of friction, we can calculate the minimum angle of repose of any body on the inclined surface. We can calculate the coefficient of friction by writing tan and angle of repose theta. That's all for today. We will meet you in the next chapter. Thank you for watching.

Transcript for:Understanding Dynamics: Moments and Equilibrium

Transcript for:
Understanding Dynamics: Moments and Equilibrium