good morning everybody today we will start with the units physical quantities and vectors this is the first lecture of university physics for engineers and other fields of science so what we have is in that chapter we will discuss the nature of the physics we will discuss the experiment we will discuss the theory we will discuss the fundamental principles and also we will learn the four steps in order to solve any physics problem this is very important if you follow that four steps it will be very easy for you to solve the physics problem and then we will see three fundamental quantities of physics we will discuss the units we use to measure this fundamental quantities in addition to that we will see how to work with units and significant figures in our calculations and we will see how to add and subtract vectors graphically and by using vector components there are two methods during that lecture we will finish graphically vector adding and subtraction but vector components will be discussed on thursday i see in addition to that we will see within that chapter there are two ways to multiply vectors the scalar or dot product and the vector or cross product okay we will discuss all the things within that chapter let me tell you something here this chapter is very important but another important point within that chapter that you will use the knowledge learn listen that chapter everywhere in each chapter of this course also in physics tour everywhere you will use that information in your physics courses in addition to that this information this vectors units will be very helpful for you for your own courses in your own department for this reason i strongly suggest you to concentrate on the transparencies and try to learn or if you know try to remember all the important topics in that chapter now we will discuss the nature of the physics so what is physics physics is an experimental science so we do experiments to understand the phenomena of the nature then we see patterns that relate to phenomena of nature so these patterns what is pattern you can consider like models okay to understand the phenomena of the nature so these patterns are called physical theories so you do experiment and then you develop a model and this model is called as physical theory but if these physical theories are very well established or widely used then they are called as physical law or principle in order to be physical law or principle each theory must be very well established and it must be widely used okay this is very important here one example to the experiments this is leaning tower of pisa you know very famous and this is a church just in the adjacent of this leaning tower so according to the legend galileo investigated falling objects so let's consider that galileo staying here and then he dropped some objects and then he investigated falling objects by dropping them from this tower in addition to that within that church that cathedral let's say uh there is a swinging chandelier swinging chandelier means within that church and he studied pendulum motion what is pendulum pendulum is sarcasm you can consider like this this is pendulum motion he did experiment and then he put some theories to explain that experiment but in order to have physical law or principle these theories must be very well established and must be widely used another example to the physical experiments in our um country in our culture let's say this is a picture from the creatine observatory it was in istanbul okay you see many guys here and they are very good astronomers and they were measuring something in that time so doing experiments and here you see a picture of a madrasa from mardin as much as i remember the name is casimir madrissa i think from artuklo and ako at times this style is mainly such a plum addresses style in many central medicines you can find such water pools so do you know what is the aim of this pool there is nothing on top of that pool so during the night this pool behaves like a perfect mirror okay then you can see the stars and the position of the planets on the surface of that pool so you can measure the distance between these stars you can measure the distance between the planets okay so you can do experiment this was very old method in astronomy experiments now we have planck spacecraft this is designed to study the faint electromagnetic radiation what is feigned electromagnetic radiation ozone so left over from big bang 13.8 billion years ago so we would like to investigate electromagnetic radiation so what do you see here there is a perfect mirror you see this is perfect mirror of the spacecraft perfect mirror here okay just 1000 years ago and perfect mirror of the spacecraft and here you see technicians and here you see the reflection of these guys here you send this spacecraft to the space and you collect the electromagnetic radiation so method is i mean the idea is same light electromagnetic radiation comes from space to the surface of this perfect mirror okay so the mechanism is same here another type of experiment very new one this is an astronaut this is international space station this is ers and this international space station iss is traveling around the earth and there are physicists there are technicians within that iss and they are doing experiments okay for example this guy is outside of the iss and repairing something physicists are doing experiments now let me discuss the solving problems in physics we have a problem and we would like to solve it there are four important steps here we shortly call it i see now i will explain each step the first one is identify the second one is set up the third one is execute last one is evaluate so for example you have problem in this book or somewhere in in another book so have to solve first of all identify the relevant concepts target variables and known quantities what do we have is in the problem first of all identify them and then set up the problem so choose the equation in order to solve that problem which equation can help you just set up this one and then draw a sketch of the situation this is the setup step of the problem solving strategies and the third step is execute the solution so this step is completely related to the mathematics okay so this first and second step are related to the physics and this step where you do the math then finally evaluate your answer whether your result is meaningful or not okay you have to compare your answer with your estimates this is very important step sometimes you can get very bad result and they can be meaningless okay so you have to evaluate your answer you have to evaluate your solution this is very important and if you check the examples within the book in young and friedman you will see that each problem solved each example so this that method ic okay identify set up execute evaluate i will show you one example within the transparencies then let me continue with the idealized model we are physicists and sometimes problems may be very very complicated okay so then we have to simplify the problem in order to analyze them so here i will show you one example for the idealized model this is real baseball in flight okay it is flying like this this is baseball but have to idealize this one this is the idealized model of the baseball so in real case baseball has some volume okay and it has some certain direction and there is a gravitational force on ball of course it depends on the altitude and this is the direction of the motion of the baseball since there is a volume of the baseball there is air resistance and wind exerts forces on the ball right but in idealized model of the baseball there is no air resistance we have just point a particle so we treat the baseball as a point object as a particle okay so then there is no air resistance we omit the air resistance in the idealized model this is the direction of the motion this is again gravitational force on ball and it is constant okay so here gravitational force depends on altitude look at this one here there is a mass of uh this part of baseball there is a mess of this part of baseball so distance from the ground to that part distance from the ground to that part are different okay but here if you have a single object point object or particle then the distance from the particle to the ground is constant so gravitational force is constant so in real case the problem is complicated to solve it in idealized models you can solve the problem much easier do you have any question here in that part and let me continue with the standards and units we have three fundamental quantities of physics which are length time and mass and their units units of these standards are defined by international system si very famous name so length has unit of meters time has unit in seconds mass has unit in kilograms okay there is another unit system cgs in turkish j guesses okay instead of meters centimeter instead of second again second and instead of kilogram we use gram for the mass okay in cgs unit system but there is another unit system the british system so in the british system they use inch okay especially in engineering inch is very important it is widely used so one inch is equal to 2.54 centimeter and for the force instead of newtons in the british system pound is used and it is equal to that number and you know mile this is very important also in navigation okay one mile is equal to 1.6 kilometer roughly this is a speedometer from a united states built automobile what do you see here there are two scales mile per hour and kilometers per hour mile is used in united states and in some countries so now let's come to that this standards and units so land time and mass what is this standard length what is this standard time what is the standard mess so what is one meter what is one second who defined them so this is very important question the one second is defined with the frequency of microwave radiation this is necessary to excite cesium atom here there is a cesium atom okay this is the electron the synthesis human and microwave radiation electromagnetic radiation with the frequency of exactly this cycles per second comes to the cesium atom and then it causes the outermost electron of a cesium atom to reverse its spin direction okay so atomic clock uses this phenomenon to tune microwaves to this exact frequency so one second is defined as the time required for this number of cycles of this microwave radiation frequency of that electromagnetic radiation it is started from 1967 okay until 1967 in order to define the time we used average time between successive arrivals of the sun at its highest point in the sky okay so from 1889 until 1967 we used the sun but now we are using much accurate standard which is used in atomic clocks this is the standard for the time and standard for the length so what is one meter one meter is defined with the distance that light travels in vacuum in one over this second light travels exactly 300 000 kilometer in one second so this is the measuring meter and what about the standard of the mass until 2009 until the last year the standard of mass the kilogram is defined with the mass of a particular cylinder of platinum iridium alloy here you see a cylindrical shape of platinum iridium alloy like battery you can see okay but pure platinum iridium alloy it is one kilogram but it changed in 2080 now the kilogram is defined in terms of three fundamental physical constants speed of light remember that speed of light gives us the standard optimeter and frequency of cesium atom frequency of cesium atom gives us standard of the second for the time and we have planck constant so this three important fundamental physical constants now gives us the standard of the kilogram starting from 2019. in the book you will see that this standard is defined with that one but it is not updated so this is the up-to-date information do you have any question here in that point i have three transparencies and then i will have a short break okay so now let's discuss the unit prefixes prefixes means here micrometer it is prefix this is meter prefix milligram prefix kilogram prefix okay gram nanosecond second so you can convert one micrometer to the meter okay this is the size of some bacteria and living cells one kilometer can be converted to the meter okay and one milligram can be converted to the kilogram one gram can be converted to the kilogram one nanosecond can be converted to the second 10 to -9 seconds so here i have already discussed the british system now um let me give you some typical lens in the universe so this is the limit of the observable universe 10 to power 26 meter and this is the distance to the sun 10 to power 11 meter and this is the diameter of the earth 10 to 7 meter 1 meter 2 meters human dimensions and now here we have 10 to minus 5 meter or 5 microns diameter of a red blood cell and if you go further we have 10 to minus 10 meter this is almost one angstrom okay smaller than one nanometer one number is 10 to minus 9 meter 10 to minus 10 meter is one angstrom this is more or less radius of an atom okay one angstrom two angstrom 2.5 angstrom this is the radius of an atom and if you go further 10 to minus 14 or 10 to minus 15 meter which is shortly called as one fermi radius of an atomic nucleus okay there are protons and neutrons here here we have blood cells the size is around 5 microns you can see the this images by using microscopes optical microscopes but what about the atoms you cannot see atoms by using optical microscope in order to see atoms you have to use scanning tunneling microscope or transmission electron microscopy we have to use electron microscopes so let me continue with the unit consistency and conversion first of all let me choose the laser pointer this part is very important when you are solving the questions okay so students usually do some errors and mistakes within the calculations this sometimes comes from the unit inconsistency and errors in the conversions so you must be very careful be sure you are adding apples to apples this is very important and the terms to be added or equated must always have the same units so always carry units through calculations so for example you are carrying out a calculation always use units okay for example here we have a question if a body moving this constant speed v travels a distance d in a time t these quantities are related by the equation here the distance is given by velocity times time right so the unit of the distance meter what about the unit of the velocity meter per second right what about the unit of the time second so always use units within the calculations for example let's consider that distance is 10 meter and time is 5 seconds and velocity is 2 meter per second so if you put the units here so what you will see this second comes from the time will cancel the second then we will have meter here on the left side we also have meter okay and equation must be dimensionally consistent meter meter if you are second on the left side you should have second on the right side if you have joule on the left side you should have joule on the right side okay don't forget this so if you use the units within your calculations you will get much correct results okay another important thing is that conversion so for example here we have three minutes and we would like to convert this three minutes to the seconds so how to convert this one so during conversions you must be very very careful one minute is equal to 60 seconds so put it here this minute will cancel this minute and we will have second year 60 times three we will have 180 seconds so the converted minute to the second okay this is the unit for the time this is unit for the time so we have unit consistency okay so these things are very important in your calculations sometimes students especially students in the first year of the university usually do not care about this units and conversions just multiply 3 with 60 okay then just write 180 without any unit or just put three without any unit so if you do these things in your university courses you can get bad results or errors in your calculations for this reason i strongly suggest you always carry units in your calculations any question here in that part okay then let's discuss the uncertainty in your calculations and significant figures uncertainty means baylor sizzlic in turkish or error hathaway what is the opposite term for the uncertainty accuracy casino okay so what about the significant figures significant figures means that in turkish online or in english meaningful digits okay so i will give you some example here we have a cover of book for example and we would like to measure the thickness of this cover okay i would like to measure the thickness of that cover and this thickness is 2.91 millimeter so 2.91 millimeter we are talking about two millimeter and we are giving additional two digits here 91 millimeter 0.01 millimeter so you say that accuracy is given by three digits to nine one so we have three significant figures okay with this we mean that the first two digits are known to be correct so this one 2.9 millimeter while the third digit is uncertain okay so the accuracy of the third digit is not so good as this once so the last digit is in the hundredths place so the uncertainty is about 0.01 millimeter this hand it is not so easy to accurately measure this last digit now another important point for example two values with the same number of significant figures may have different uncertainties so here we have one two three digits so three significant figures okay here look at this one we are talking about a distance given as 137 kilometer one two three significant figures okay three significant figures here three significant figures here here the uncertainty is about 0.01 millimeter but here the uncertainty is about one kilometer so instead of 137 you can measure 136 or 138 okay we have one kilometer uncertainty but here uncertainty is about 0.01 millimeter at the last point here with the significant figures distance given by 0.25 kilometer has two significant figures here you can see that there are three numbers but zero to the left of the decimal point does not count okay if you have zero here you don't count this one here we have one and two significant figures okay so if this number is given by 0.250 then we have three significant figures okay uncertainty is given by 0.001 here uncertainty is 0.01 okay so these are the uncertainty and significant figures very important in calculations i will give you some more examples so how to use significant figures for example you are doing multiplication or division so look at this one here just concentrate this this transparency here we have a number with three digits after point okay so significant figures three so here significant figure two seer significant figure here i can measure precisely here i can measure precisely three digits after the comma but here i cannot measure precisely 2.2 okay uncertainty is 0.1 so the result here i mean in terms of significant figures must be like this the result can have no more significant figures than the factor with the thieves significant figures here on the left side this number has the fivest significant figures significant figures are two on the right side result can have only two significant figures so here we have one two significant figures okay so the the fifth accuracy on the left side defines your accuracy on the right side so again here for example in multiplication so here we have one two three four five six significant figures here we have three significant figures and result look at the result it can be three significant figures you cannot give six significant figures on the right side because here we have only three significant figures is this part clear if not please let me know now let's continue with the addition or subtraction for example here we have this number plus this number minus this number and we will have result so look at this one after the decimal point here we have just single number you see just 0.2 but here after the decimal point we have 1 one five three three numbers three digits after the decimal points here one digit after the decimal points and here two digits after the decimal point and the result can have only one digit after the decimal point due to the this number with the largest uncertainty this has better accuracy than this one and this has better accuracy than this one so this result can have accuracy as this guy okay is it clear so what about the uncertainty or errors or accuracy in calculations and significant figures they are very important in calculations here there is one example from all times this is train station okay and this is a train so as this train mishap illustrates even a small person error can have spectacular results maybe you have watched the dragon grief flight to the international space station during this summer you know spacex company sent two astronauts to the international space station by using dragon creev right dragon capsule so this dragon capsule went to the space and then connected to the international space station so uncertainty is very very important even very small person error can have spectacular results in technology okay for example we can consider guns or fighting jets or unmanned armored vehicles for example you shoot somewhere or you send a missile to somewhere let me draw here here there is a missile station and there is a rudder on top of it and here there is an enemy okay you have to hit that target and then you send a missile so missile should hit that point okay is it clear so missile should hit that point and uh let's consider that here there are your friends and you mustn't hit them so in that case let's say the distance is one kilometer for example so even a small percent error can have spectacular results okay sometimes this guns this missiles can hit some civilian places okay so this is very important for many field of science and engineering and many field of life okay so let's continue with the vectors and scalars scalar quantity can be described by a single number just magnitudes for example temperature for example energy okay we are talking about temperature plus 5 degrees or now plus 30 degrees celsius or minus 20 degrees celsius okay just numbers just magnitude and unit but it has no direction okay scalar quantity has no direction it has just number just magnitude however a vector quantity has both a magnitude and a direction in space again let's have a look that example this guy is walking on a wintry day okay the outside temperature is let's say minus 20 degrees celsius and this temperature is scalar and there is a wind in that direction okay so the magnitude of the wind is written here 15 kilometer per hour and what about its direction it comes from the vest okay a vector has some certain direction okay so this is very important uh different difference between scalar quantity and vector quantity this is given by just a magnitude and this is given by balls and magnitude and direction in space so this in the book young and friedman and also within the lecture notes transparencies in that course we will use a vector quantity which is presented in bold phase italic bold with an arrow over it you see this arrow here and the magnitude of this vector is shown by italic without error or with this symbol we use magnitude okay this is vector this is magnitude this is vector this is magnitude okay don't forget this one so this is the main difference between scalar and vector so force for example vector momentum is vector okay temperature is scalar energy is scalar so you will see many vector quantities we will discuss them later on let's discuss the displacement very important term in physics especially for physics 1 displacement is a change in the position of an object in turkish yard here look at this one this is the position one initial position or starting position or first position and this is the position two ending position or second position or last position you can say so you move from that point to that point and this is the displacement and displacement is a vector okay displacement is a vector don't forget it has magnitude for example the distance is one kilometer let's say and it has certain direction magnitude one kilometer direction is this one so this is the displacement another representation of the displacement this is the first position this is very important listen carefully this is the first position and you move like this okay and then finally your last position what about your displacement this is not the displacement displacement is this one okay you change your position from this place to this place this is the displacement so this placement does not depend on the path taken even if the path is curved it doesn't matter so now let's have a look this one this is the first position and you follow this pass and finally you come to that point so first point and second point or last point are same so total displacement is zero okay displacement is 0 in that case now how to draw the vectors we draw vector as a line with an arrow of hat at its tip so this is the vector this is the arrow head this is tail in turkish this is head bush okay don't forget this one head tail tail hat so the length of the line shows the vector's magnitude this length shows the magnitude and the direction of the line shows the vector's direction direction is this one so here we have displacement a and we have another displacement which is shown by a prime okay since its direction is same since its magnitude is same this second displacement is equal to the first displacement okay so if any vectors have equal magnitude and same direction they are equal okay don't forget this one so what we have here uh magnitude is same like this one and this one but the direction is opposite okay since the direction is opposite this this new vector b is equal to minus a they have same magnitude but direction is opposite this minus here shows the opposite direction any question here then let me continue how to add two vectors graphically we can add two vectors by placing them head to tail so look at this one vector this is the hat of the a vector and i have another vector which is given by b and i would like to add them to each other so put the tail of b to the head of a head to tail head to tail okay then drove the resultant vector c a plus b okay so you can add them also in reverse order for example here we put the b to the head of the a but here we will put a to the hat of b again head to tail head of b tail of a head to tail method and again the resultant c vector is given by b plus a and b plus a is equal to a plus b because this blue b vector and this blue vector have same magnitude and same direction for this reason a plus b is equal to b plus the order doesn't matter in vector addition we can add two vectors by placing them tail to tail and constructing a parallelogram like this one here i have a vector here we have b vector okay tail of a tail of b okay we add them tail to tail and here you can draw a parallelogram for a and b vectors okay so in general what do you see here take this a vector and carry this vector here okay again let me draw maybe you will better understand i will draw the a vector okay so what do you see here this is the hat of the b vector this is the tail of a vector again head to tail method and we have resultant c vector what happens if they are parallel and anti-parallel we will discuss these conditions if they are parallel to each other like this one let me choose again the laser pointer here i have a vector b vector and a plus b gives us the c resultant vector if they are anti-parallel for example here i have a vector in that direction it has certain magnitude and this is the b vector it has certain magnitude but its direction is opposite to the a and the resultant c vector is given by a plus b so a plus b is this one okay so actually magnitude of c is given by a minus b and now let's consider that we have many vectors more than two vectors and how to add this many vectors graphically so to find the sum of these three vectors here i have a vector b vector c vector they have different magnitudes and they have different directions so you can add them in any order it doesn't matter so you can do like this a and b head to tail and then resultant is d then c plus d d is the resultant of a plus b and plus c so this is the resultant vector this is one method or you can do like this a b head to tail and b c head to tail so this is the resultant vector okay or you can do like this b plus a plus c head to tail head to tail so this is the resultant vector so you can add more than two vectors graphically with that methods do you have any question here in that part i will continue with the subtracting vectors here we have here and here we have b vector okay so a minus b will give us a plus minus b you will see that so what was the minus sign here minus sign is showing us that the opposite direction this is the b vector minus b has same magnitude with that one only its magnitude is opposite okay so now let's do that here on the left side i have a vector you see a vector and b vector here put b vector here so this is a minus b okay so look at the right side i have a vector here and we have b vector here so this is the but but this is plus this is minus in case of minus look at this one in case of minus we add them head to head in case of plus we add them head to tail okay here we have a vector here we have b vector put a here put b here head to tail and this is the resultant vector a plus minus b here a vector and b vector we are doing subtracting for this reason we have to combine them head to head and then resultant vector is this one so what do you see here a plus minus b equal to a minus b so because resultant vectors have same magnitude and same direction so now another important property of the vectors and then i will finish with that example our lecture will be finished so multiplying a vector by a scalar for example you have a vector and you would like to multiply this a vector with a scalar number for example 1 or 2 or 3 or 1.5 okay so magnitude will be number times magnitude of the vector and the direction will not change if it is positive number okay so here we have a vector and i multiply this a vector with 2 then the magnitude is twice as long as a okay but the direction is same if you multiply this vector by a negative scalar number for example we multiply this a vector with minus three first of all the magnitude will be three times bigger or longer okay this is three times longer compared to the a vector but its direction is changed due to the negative number here this is the multiplying a vector by a scalar number then i will finish my lecture with that example here let's consider that a cross-country skier just a cross-country skyer so this is river and then this is the position of this car skyr first of all starts from that point and then she goes one kilometer this is the north south east west one kilometer along the north and then it goes over bridge here over the river two kilometer to the east okay so this is the resultant displacement so the result will be more than two kilometer the result will be more than one kilometer and the result will be less than three kilometers okay you can estimate this one without any calculation so how to calculate magnitude of this displacement and how to calculate the angle here in order to calculate magnitude and its direction we have to use trigonometry okay you already know this information from your high school years and by using that information we will calculate the magnitude of the resultant displacement and also we will find its direction look at the sign here this is the east this is the north and this displacement is something like this okay between east and north right so but which angle between east and this resultant vector or which angle between north and this resultant vector you can calculate this one the distance from starting point to the ending point is equal to the length of the hypotenuse actually this is hypotenuse right so you can calculate one kilometer square plus two kilometers square is equal to displacement square okay so you can calculate 2.24 kilometer this is the magnitude of the resultant displacement so what about the phi angle i mean the direction of this vector displacement vector you can calculate tangent phi phi is here tangent phi can be calculated opposite side over adjacent sides okay so look at the calculation i am using the units you see units are here two kilometer one kilometer so the result is unit less because kilometer cancel this kilometer so the result is two tangent if tangent phi is equal to two then phi is 63.4 degrees you can do it by calculator so then we can describe the direction of this resultant vector 63.4 degrees east of north okay so this is the north so vector is like this 63.4 degrees east of north or you can you can consider like this just complete 90 degrees here then this angle here between east and this resultant vector will be 26.6 okay so this is the addition of two vectors at right angles do you know what is right angle right angle sanders next we have components of a vector but here i will stop and then we will continue on thursday to discuss the components of a vector if you have any questions please let me know in a okay maybe you are talking about right angles right angles means uh if you have two vectors at right angles you can add these two vectors with that method as i explained here and you can calculate the direction of the resultant displacement vector between east and north you can get the angles here maybe you mentioned this one but i don't know if you can tell me in detail i can repeat that