Free Physics NEET Video Lectures for Laws Of Motion

00:00:39 [Music] Till now we have studied how a particle moves and what we described as kinematics a description of motion. Now today and in the next series of three or four lectures we will look at what are called the laws of motion. And the question which we will try to answer is what governs the motion of a body. And to understand this the first thing which we do is we need to introduce the concept of force. Now uh if we try to define force uh I think we'll be going in round and round circles. Maybe we'll use some

00:01:48 words to define force. But if we look at it, what we can say is that force is a quantitative measure of mechanical interaction of material bodies. That means if we have two bodies and they interact with each other then they interact with each other through a quantity called force. And one thing we realize which we observe in nature is this force could ensue between bodies either when the bodies are in contact or in some cases force could also be there. If the body, even if the bodies are not at

00:03:08 contact or they are not touching, then force could be conveyed through a distance. And we will look at examples of all these things. But just to illustrate if I touch the table and if I touch it I feel a force on my hand and similarly a force is being applied on the table by my hand and if I take an object and if I drop it then the object is moving and the earth is applying a force on this object even though there is no contact between the earth and this object. So therefore in both the situations whether

00:03:58 there is a contact or there is no contact if there are two bodies which are interacting with each other there could be a force between these two bodies and throughout our this series when we talk about uh force and laws of motion. We will see how do we quantify this sort of uh interaction between bodies and we will see that these interactions are quantified through some laws and those laws are what we will study during the course of these series of lectures. Let's try to characterize some properties of force. So first thing

00:04:36 what we realize is that force is a quantity which has a magnitude and this is obvious from the fact that if I press the table lightly or if I press the table very hard I feel a different sensation on my hand. So therefore in one case the force is less in the other case the force is more. So it has a magnitude but not only does it have a magnitude it also force it has a magnitude and it also has a sense of direction. So and as we have seen that quantities which have a magnitude as well as a direction these

00:05:37 quantities are referred to as vector and also what we had described earlier when we talked about these every quantity which has a magnitude and direction need not be a vector but vectors have some other properties. For example, vectors follow parallelogram law of addition or the triangle law of addition and also they transform according to a particular relation and what we find is that force does follow these law laws. So force is a vector quantity that means it will uh if two forces have to be added there'll

00:06:20 be two forces with different directions and the addition will follow the parallelogram law of addition or you could use the triangle law of addition which is equivalent. So what we do is we represent force by an arrow. The length of the arrow is proportional to the magnitude of force. And the direction of the arrow gives the direction of the force. And this particular statement which I have made that it's the length of the arrow is proportional to the magnitude of the force. This becomes more

00:07:19 pertinent when we are talking of two different forces. They will have their own magnitudes and then the length will represent the ratio of these two forces. So the ratio of the lengths will represent this ratio. So that is how we represent a force. Now one thing which we observe and this is very uh a subtle thing which we realize is and this is this comes from observation. There is no proof for this. And what we say is that the force which we see this is not dependent on the frame of reference in

00:08:03 which force is being measured. Now can we say the same thing for all scalar or vector quantities. So the qu what I'm saying is now frame of reference is as we have seen a same quantity could be measured in a frame which is fixed on the surface of the earth or something which is moving. Let us say a car is moving we measure the quantity from the moving car. And the point which we are making here is if we look at forces forces will not depend on whether you are observing the force from a stationary frame of

00:08:45 reference or a frame which is moving with constant velocity or constant acceleration or variable velocity variable acceleration whatever it is force does not depend on the frame of reference. Is there any quantity which depends on the frame of reference? Very obviously we have seen that when we look at the position vector position vector we fix a coordinate axis and we mark the position vector and it obviously depends on the frame of reference and not only position vector we have also seen velocity and acceleration which we

00:09:16 measure they are frame dependent quantities. So let's just say as opposed to position vector or velocity or acceleration which depend on reference frame in which they are being measured. And once again these this observation which we have for force this is valid in the realm of classical mechanics where we say that the speeds with which we are talking are uh much less than the speed of light. So all the arguments which we are going to talk about in this chapter and at least throughout this course uh at in the

00:10:17 mechanics part are what we call as classical mechanics which is where we are not considering the effects. So the speeds are much less than the speed of light. So now let's try to see if we have a body in contact with a second body. That means I have a body A and a body B and these two are touching. So this may be body A and this may be body B and there is a contact between these two bodies. So if we have a contact, the contact between A and B can give rise to a force. And example of such forces when we

00:11:14 see examples of such contact forces let's uh illustrate this are forces what we call as reaction forces and among them are included within these reaction forces we have things like a friction force. Whenever a body is sliding on a surface, then we see that there seems to be a force which tends to prevent the relative motion between the two surfaces. And when we have this force between two bodies or two solid bodies in contact, we call it as the friction force. In addition to this, if suppose I

00:12:07 have a body, let's say an aeroplane which is traveling in air. So then in this case, air is in contact with the aeroplane and air will put what we call as a viscous force on the aeroplane. So therefore these forces such as reaction forces, friction forces, viscous forces are examples of forces which are which arise because there is a contact between two material bodies. Another example of a contact force could be suppose if we have a dam here that is a wall and there is water on one side. Such a thing is is what we call a dam

00:13:04 where we have a wall which is preventing the water to go. Now here when water touches the surface of the dam, water will exert a force. We call this as the hydrostatic force. So this is another example of force which comes because of contact. But in addition to this, what we have seen is there are some other forces which do not require any contact between the two bodies. But once again we realize there have to be two bodies for these forces to occur. Example of this as I had already illustrated the

00:13:57 first example is the force due to gravity and we looked at it in the sense of when a body is being pulled toward the surface of earth but Newton also generalized it to universal law of gravitation. If there are any two masses they exert a force on each other even when they are close to each other and here this force of gravity we as we will see I'm just speaking in a very qualitative way right now this depends on is proportional to 1 / r² where r is the separation between the two bodies in fact the it's not only the

00:14:36 magnitude the direction is also specified by the law of gravity and we will look at this later. But in addition to gravitational forces, there are forces due to uh between two charges. If we have two charges, a charge Q1 and a charge Q2 then there is a force between these two charges which we call as the electrostatic force. And then we also have in addition to this we have electro magnetic force which is experienced by a charge which is moving in a magnetic field. Now once again for these electrostatic and

00:15:24 electromagnetic forces there is no contact. These forces occur through a distance. Now let us try to see what is the qualitative effect of a force. And the simplest way in which we can explain is that a force tends to push or pull a body along its line of action. So that is the I think the simplest way in which we can describe a force. Now once we will later on we'll also see that along its line of action a force tends to push or pull. But if we look at the effect of force from a point other than its line of

00:16:25 action then we will also see it tends to rotate a body about a point which is not on its line of action. But this discussion we will postpone right now will come in when we talk of rotational motion and motion of rigid bodies. So that is in a qualitative way what we see is so but what happens when we say a force tends to push or pull a body what does it actually tend to do to the body. So by pushing or pulling what the force tries to do is it tries to alter the state of motion of a body. This is the effect if I look at it

00:17:16 in terms of kinematics what the force does to a body. For example, let us look at this pen. This is lying on my hand. It is at a state of rest. I apply a force and as I increase the force I see that the pen starts to move. So that means the effect of this force is that it tends to alter the state of motion. If the body is at rest then it will tend to start the motion of a body or vice versa. If a body is moving then we can bring it to a state of rest by applying a force. And so now this is just a

00:17:58 qualitative way of trying to see what a force does. The quantification of this what we have said qualitatively the quantification of these statements. This is what we will study by laws of motion. Laws of motion will quantify how the effect of force in terms of the state of motion of a body. But before we do this, let us explain, let us define some more basic concepts. So the first thing which we define is a concept of a particle. And what we will say is a particle is an entity of finite mass but but infinitisimal size. That means

00:19:08 at a time at a time particle occupies only one point in space. So if we are talking in terms of coordinates what we can say is the particle is at XY Z the spatial location at time t. So this is how we idealize a particle. Now this is an idealization. I use the word idealization because everything which we know has a finite size. So when we want to consider the motion of a body such that its physical size is not important then we idealize it as a particle. And for example, when we talk of motion of a

00:20:03 ball or a freely falling ball as we have seen in projectiles, then the ball is assumed to be a particle. And at least for the purpose of the next few lectures, we will assume all the bodies on which we are applying the laws of motion are particles. And this is as opposed to for example let us say there's a rod of length L and we want to study the motion of this rod suppose I'm applying a force at this point and if I apply a force at this point then it is possible or maybe at some other point there's another force

00:20:55 being applied Then different points in the rod may have different velocities and in that case we cannot idealize the rod as a particle and as we will see later we will talk about it as a rigid body. Uh we can maybe at this point just define the concept of a rigid body which will come in much later but I want to at least get you to start feeling the notion of a rigid body. A rigid body is a set of particles such that the distance between any two particles is always the same. Now this will not mean that the

00:21:51 particles have all all the particles on the body have to move with the same velocity as we will show but at least just keep this definition in mind and currently we will just focus on particles. Now when we say we have a particle of mass m and the main thing is when we talk of a particle the mass of a particle is finite. It is not uh infinite decimal and we observe the motion of the particle from some frame f. What we find is the particle has a velocity V. It has an acceleration A and maybe we'll start it also has a

00:22:45 position vector R. Now what we also find is the mass of the particle. This is always constant. And this again comes when we are talking in terms of our classical mechanics. Mass of our individual particles will always assume to be constants. And if we talk of two particles, the sum of their masses will be equal to if that particles a and b then ma plus mb will be equal to if both of them are combined together the mass of the new body will be equal to ma plus mb. So masses add linearly when particles are combined.

00:23:28 So now we define we have seen mass of a particle which is constant and this mass does not depend on the frame of reference. We have a quantity velocity of the particle which we have already seen and using these two we define a new quantity and which is critical to our laws of motion and we define a quantity called momentum. We use a symbol P with a vector. In your textbooks, you may find a bold-faced P which will represent this quantity momentum. And momentum is defined as so we'll say P is defined as the product

00:24:15 of mass and velocity. So that means we are multiplying a scalar with a vector. So the net resultant quantity is also a vector. So P is a vector quantity and it's a product of mass and velocity. Now let's start looking at the laws of motion. This definition of momentum we have seen we will be using it when we disc when we come to our laws of motion. Now what we observe is that if a body if a body is at rest then we a force is required to make it moving. And similarly, if a body is moving, a

00:25:32 force is required to bring it to rest. But the next question which we ask is it is very clear a body at rest to make it start moving force has to be applied. If a body is moving if you want to stop it a force has to be applied to it. But then the question comes if a body is in uniform motion. We have explained this before but let's try to understand this because we will be using this term uniform motion again and again. Uniform motion means a body moving in a straight line or along a straight line. We can

00:26:38 use whatever with constant speed. So if a body is moving all along a line and its speed let's say v is equal to constant then we say this is in uniform motion and you'll easily realize this also implies that the velocity of the body is constant. So uniform motion is the same as saying the velocity is constant or we will say it is moving in a straight line with constant speed. All these three things are synony synonymous. Now the next basic question we ask is is a force required to maintain the state

00:27:37 of uniform motion. That means I have got a body which is moving in uniform motion or with constant velocity or with constant speed or a straight line. Do we need a force to be applied on this body so that this state of motion can be maintained? And for a long time, Aristotle, the Greek philosopher who was in 322 BC, he had his ideas that to keep a body moving at uniform velocity. a force is needed and these ideas are what people followed for a long time but it turns out this was wrong. So let me while

00:28:38 Aristotle said this that a force is needed let's put a cross on this to show that this was a wrong notion and basically it was not Aristotle's fault what he understood was if you see this practical thing that if there is something which is moving and if a body is there you give it a push and leave it then it comes to a rest. So therefore to maintain its motion of uniform velocity a force needs to be applied. But what Aristotle did not consider was that because this body is in touch with the

00:29:16 body second body in this case my hand below the hand applies a force of friction and that is what is stopping the body and this was not uh considered by Aristotle. So there is a friction force which is when there are two solids in contact or a viscous force which tries to oppose the relative motion but this was not considered. Then it was Galileo who was from Italy from 1564 to 1642 who first observed this and he refuted Aristotle's idea and what he said was that to for A body to maintain its state

00:30:19 of uniform motion. No external force is required. And how Galileo got this? Let's try to see there was some very nice insights uh because of which Galileo could make these observations. What let's look at a motion of if there are two inclined planes and what we see is if a body let's say there's a ball which rolls down the incline. We take this example because when a ball rolls down the incline the friction force is very small. So when it rolls down the incline because of the gravity the

00:31:13 acceleration as it moves down this is positive. The the speed of the ball keeps on increasing. But when it moves up the incline then the acceleration is negative. So if the same ball is starting with some speed here and it moves up the incline then there is a negative acceleration. So now if we try to reduce the angle slowly and we come to a state where there is a level surface. So there what will happen from if there's positive acceleration here negative acceleration here then on case of a

00:32:01 level surface it is it will be very intuitive to expect that the acceleration in this case will be zero. That means if the ball is moving with acceleration with a on a plane surface then its acceleration will be zero. So it will just keep on moving without any force being applied to it. So this was the idealization how uh he reached this and then he also did a thought experiment. You take a ball and you put two inclines together as we have done there. Of course, we are looking at the motion separately. If

00:32:43 this balls if this ball comes here and let's say this angle is theta this angle is alpha it travels a distance d1 down the first incline and after coming here it starts to go up and the distance it travels up the incline is d2. So what is observed is if theta is equal to alpha then d1 is nearly equal to d2. So then what and also what you observe is if angle if angle alpha is greater than theta then the distance d2 is less than d1. That means if this is more steep it goes up a lesser distance. So we first take alpha which

00:33:34 is greater than theta. We find this distance is less. Then we reduce alpha. We bring it equal to alpha. We find this distance is equal. So now when we reduce it more so we take alpha less than theta then we find d2 is greater than d1. And then suppose if alpha is made zero then what one would if we keep on sort of uh looking at in the same way then what we find is that we would expect this distance d2 to go to infinity which would mean that if this angle alpha is zero then once the ball comes here it

00:34:15 keeps on moving on this surface which would say that no external force is required. So what Galileo said was that if a body is in a state of so what Galileo's observation was if a body is at a state of rest or in uniform motion then both these states are equivalent and no force is required to maintain these stats. So that means whether the body is at rest or is at uniform velocity, the body tends to maintain its own state. And this property of the body to maintain its state of rest or uniform motion.

00:35:48 This property we refer to we call it a special name this is called inertia. So, so the basically what we can say is a body does not change its state of rest or uniform motion. Unless an external force is applied on it and this essentially is also referred to as Newton's first law of motion. Well, historically it happens. In fact, Newton was a British scientist and Newton was born in 1642, the year in which Galileo died. But what Newton did was he compiled he studied motion of bodies and he gave what we term as three laws of

00:37:15 motion. And the first law of motion is essentially what Galileo had already said. But since Newton compiled all the laws. So therefore we refer to this as the first law of motion or Newton's first law of motion which is valid for a particle. And what Newton's first law essentially we have stated that and in Newton's turn the terminology the first law says that each body continues to be in a state of rest or uniform motion. Unless compelled by an external force to act otherwise. Now here what we have that means what we are

00:38:33 assuming is if a body is in a state of uniform motion there is no external force acting on it and we should probably qualify this statement slightly because when we say there is no external force it gives a sense of feeling that no force is acting on a body but what we also realize is that it's possible that two forces are acting on a body and the net resultant of these two forces is zero which is equivalent to saying that there is no net force acting on a body. So therefore we should instead of saying

00:39:08 it that no force acts maybe the correct way to word it will be that there is no net force acting on a body or some of the external force acting on a body if they are zero then the body will tend to be in its state of uh rest or uniform motion. So the uh instead of individual forces being zero if the net force different forces may act on a body but if their resultant is zero then also this law will be valid. So and other thing which we realize is that when the body is in rest or uniform motion is there some common kinematical

00:39:53 quantity which defines these two states. a body at rest or a body in uniform motion and the common kinematic quantity which we can see is acceleration which in both these cases whether the body is at rest or the body is in uniform motion has got to be zero. So therefore what we can deduce is if the net external force on a body is equal to zero then its acceleration is equal to zero. And this may be another way or a quantitative way of looking at the first law of motion. So now we could have two types of

00:40:55 situations. There are two types of situations we could handle. The first one is if we know that sum of all external forces acting on a body is equal to zero. Then we can say its acceleration is zero. But normally in real life finding whether sum of all external forces are is zero or not may not be so obvious. But from a measurement viewpoint more often what we can easily see is or easily measure is that we may know that if acceleration of a body can be measured because as we have seen in kinematics all we need to do is

00:42:09 measure the position. The rate of change of position that gives us the velocity. Rate of change of velocity gives us the acceleration. And we may not know all the forces acting on the body. So therefore in such a case what we say what we can say from the first law is that if acceleration is zero then sum of forces or some of we'll clear we'll make it external forces acting on a body have to be zero. So let's let us take an example of this. Suppose I look at uh at the sphere which is lying on ground.

00:43:19 Then what I know is that on the sphere there's a force due to gravity which I call it as the weight and let me write it as m * g and we'll see more of this when we uh come to problems on this topic but this is how we write and so this is one force which is being applied on the sphere. because of the earth. Now we also see there's a contact on the ground and the contact on the ground we do not know what it is. Let us say we represent it by a reaction force R. Now in this case because we know that the acceleration of

00:44:07 the sphere is zero this will imply that sum of forces on the sphere must be zero and therefore this reaction force R must be equal to mg. So now this is what we sometimes is also referred to as bodies in equilibrium and when bodies are in equilibrium then they don't move and sum of external forces acting on a body is equal to zero. In fact this is a branch of uh mechanics which we refer to as statics where we talk of bodies which are not moving at all and we uh we analyze them. In fact, a whole of civil

00:44:59 engineering structures which we talk of is based on this branch called statics which is very important. We have seen the first law of motion. Let us see some more places where the first law is actually can be used to explain some phenomena. And let's look at some examples. Suppose we are moving in a bus and initially the bus is at rest and as the driver starts the bus and let's say he puts a sudden acceleration. It is observed that the body tends to fall back. And a reverse observation is felt when we are moving

00:46:07 in again in a bus or a car and there is a braking effect. The brakes are applied on the car and we find the body of the passenger tends to fall in front. How can we explain this? So in both these cases what we realize is that the feet are in touch with the floor of the bus or the car. And as the car accelerates or decelerates if it is stopping and what we find is the feet constantly touch the floor. So and because of friction there is no relative motion between the feet and the bus or the car. So therefore the

00:47:45 feet have the same acceleration. But when we look at the human body, the human body is not one single rigid body and the the top parts of the body or top part of the body when the bus starts This tends to maintain its state of rest. So while it is connected to the feet, it is not in contact with the ground. So therefore, it tends to maintain its state of rest. Whereas the feet, they move ahead. This is the case when the uh bus is starting to move the feet move ahead. The body tends to maintain its state of rest and so

00:48:56 therefore the body tends to fall backwards. Of course, as soon as it starts to fall backward, there is a muscular force acting in the body which brings it forward and it comes uh to the same state of rest with respect to the bus. But the initial reaction is that the body tends to fall backwards. And then opposite effect takes place when a break is applied. When a break is applied, there's a deceleration and the feet ex they feel the same deceleration. So when the feet feel the same deceleration, they tend to stop. But the

00:49:34 body is still in a state of motion moving forward. So that t tends to maintain its state of motion. So therefore it tends to fall forward when a sudden brake is applied and then the muscular forces act on the body and bring it to a state of rest with respect to the car. Now so what we have seen let's try to focus on this point again I referred to it that state of rest as far as the first law goes the state of rest and state of uniform motion once again uniform motion means motion at constant speed along the same

00:50:18 direction. This is very important because once the direction changes we know even if the body is moving at a same speed there's a component of acceleration which is perpendicular to the path. This we have seen earlier. So now when the body is in a state of rest or in the state of uniform motion these two states are equivalent as far as effect of force is concerned. So as far as force is concerned whether the body is at a state of rest or it is moving they are identical. And what we do is uh so if

00:51:03 this is same then what we can say is such frames of reference because state of rest or state of uniform motion will be determined with respect to a frame of reference. So such frames of reference which are either at rest or if they move with respect to each other at constant velocities which means uniform motion. Such frames are equivalent. That means if I say there is a frame A which is at rest. So I put a coordinate system X and Y axis marked on frame A. This is at rest. There's a frame B which is moving with V which is

00:52:13 constant. So these two frames are frames of the type which I have described that they are either at rest with respect to each other or moving at constant velocity. And these two frames are equivalent as far as the effect of forces is concerned. And there's a name given to this. These frames are called Galileon invariant frames. This is just a name given to this and uh you may come across this that is why we are giving this. Now we have seen the effect of what causes uh a body to move. Now what

00:52:59 we would like to know is we would like to quantify when a body is moving how fast it moves or if a particular force is applied on a body then how much will the acceleration be and this quantification is what will come in Newton's second law of motion in the next class when we discuss we will talk of Newton's second law of motion which will refer to the case when the external force on the body is not zero and what effect a nonzero force causes to a body in terms of its acceleration. [Music]