 When I was in class 11, one of my friends asked me this question. We have the earth, which is a huge ball, and we have a moon, which is a smaller ball, and the earth attracts the moon. Why then does the moon not fall into the earth? This was my explanation to him. I told him that the earth does attract the moon with a gravitational force, but we have to remember that the moon is in a circular orbit around the earth. It is not stationary. And when things are in circular orbits, they also experience another force, which is called the centrifugal force. And this is its formula. We know that there is a centrifugal force when there is circular motion, because we have all experienced it. When we are in a car and the car takes a turn, we get pushed towards the side. Why centrifugal force? So, the centrifugal force and this gravitational force, which is the centrifugal force pointing towards the center, these two forces cancel each other. And the acceleration of the moon is therefore zero, and it does not fall in this direction. It can move in a perpendicular direction with a constant speed, and there is no acceleration in this direction. This was my explanation to him. Well, this is completely wrong. And in this video, we are going to talk about this aspect of it. What is the centrifugal force? Why does this not make sense? Why does it not cancel the centrifugal force? Is it a real force or is it a pseudo force as we keep hearing? And when can we actually draw it in free body diagrams? Let us start by refreshing our ideas of free body diagrams and pseudo forces. So, for this, I will take a very common example of a block inside an elevator or a lift. So, this is a lift and this is a block inside it. We can also draw some cables from the lift. And we want to draw a free body diagram of this mass m. So, let us do that. So, for this, what we do is we draw all the forces that are acting on this block of mass m. So, let us think about the one by one. Well, we know that we have an earth and the earth pulls every object towards itself. So, there must be a way or a gravitational force acting on this block of mass m. We also know that since this block is sitting on the surface, so this surface will exert a normal force on this block. And this is the normal force in the upper direction. And if this elevator is stationary, then this is the free body diagram. But if this elevator is accelerating, then we need to draw this acceleration also in the free body diagram. We show this acceleration. Now, using this diagram and Newton's second law, we can actually find the normal force that is acting on this body. Let us do that. We know that Newton's law says that Newton's second law says that the next force on a body is equal to the mass times the acceleration. So, the next force in this case will be m minus mg. Since the acceleration is in the upward direction, normal force must be greater than mg. When mg was greater, it would be the acceleration would be in the downward direction. So, here we can write n minus mg, n minus mg is equal to ma, is equal to ma. And using this equation, just rearranging, we can say that n equals mg plus ma, mg plus ma. So, this is the normal force. We can actually measure this normal force if we have a weighing machine here and we see it's reading. Now, weighing machine actually measures the normal force. And if you see the reading, it will be equal to mg plus ma. So, this is how we draw free body diagrams. I hope it is refreshed now. Now, let us look at what would happen if we change our frame of reference. If we go inside the lift and observe this block and try to draw the free body diagram of the same block, let's see what happens. So, this free body diagram is with respect to this person. Let's call him person A. So, with respect to person A. So, in this case, again this person knows that there is an earth and there will be a force of gravity in the downward direction. So, he will draw this force. He also knows that there is a normal force and that normal force is going to push the block upwards. So, he is going to draw that as well. But this person is not going to see the acceleration of the block. Why? Because he is also accelerating upwards. He is inside the lift. So, with respect to him, this block is stationary. So, there is no acceleration. So, if he uses his free body diagram and tries to make an equation, what he will get is n equals mg. Wait a minute. This is different from this. And we know that this is correct because the weighing machine is going to show, mg plus map, we have a weighing machine here. This is what it is going to show. So, this must be incorrect. So, are the Newton's laws not working? Right, they are not working. So, this kind of a frame of reference where the observer is accelerating is known as a non-inertial frame of reference. This is just a fancy name. What we need to remember is whenever the observer is accelerating, then Newton's laws don't seem to work. We cannot simply apply Newton's laws. Well, what can this person do now? Should he give up all hope of Newton and his laws and stop trying to draw free body diagrams? Well, that is one way to go about it. But another way is to cheat. Let's see what I mean. This person A knows that the normal force should be equal to mg plus ma, but he is only getting normal force equals to mg. So, if he simply drew an additional force of ma in his free body diagram, he would get the same result. What I mean is let's say this person decides that I am going to draw my free body diagram, going to draw mg as before. I am going to draw normal as before, but this time what I am going to do is draw an additional force in the downward direction. What this will do is this will make sure that my equation comes out to be the same as this. You can check. He knows that the acceleration is zero. So, the net upward force should be equal to the net downward force and thus n should be equal to the net downward force, which is equal to mg plus ma. And this additional force that this person added is what we call the pseudo force. Why? Because it's cheating. There is no such force like this. This person is just drawing it to make sure that Newton's laws work to forcefully apply Newton's laws. So, what is a pseudo force? A pseudo force is a fake cheating force that we apply to a free body diagram to force Newton's laws to work. In which frames do we need to apply pseudo force? In non-inertial frames. These are the frames where Newton's laws don't work by themselves. And these are generally the frames where the observer is accelerating. I hope that is clear. Now, we can come back to our original case of looking at a body which is undergoing circular motion. For example, the moon. We can see what happens there and we can look at it from both the frames. From inertial frames where the observer is not accelerating and from non-inertial frames where the observer is accelerating. So, if we have the moon here and we are drawing its free body diagram from a frame of reference which is not accelerating. Let's say we are outside. We are on the earth and we are drawing this free body diagram or we are in space and we are drawing this free body diagram. So, we will draw the gravitational acceleration towards the earth. And is there any other force acting on the moon? Well, no. There is no other force acting on the moon. Is the moon accelerating? Yes, it is accelerating. If you remember, a body in a circular motion, body that is undergoing circular motion, uniform circular motion does accelerate. Even though its speed is not changing, its velocity is changing. The direction of velocity keeps changing from one point to the other. And that acceleration which we have derived is called the centripetal acceleration. So, there is an acceleration and it is towards the center of the circle, in this case towards the earth. So, this is the complete free body diagram of the moon. We don't need centrifugal force. In fact, it is incorrect to draw centrifugal force because there is no such force. No one is applying centrifugal force on the moon. The earth is applying the gravitational force and that's it. And because of this force, there is an acceleration called the centripetal acceleration. So, using this, we can get the equation for the moon that fg, there is only one force. So, this is the net force is equal to mass into acceleration is equal to mass of the moon into the centripetal acceleration which is m into v square by r. And we are done. This is the correct free body diagram of the moon. Now, when the centrifugal force come into the picture, let's see. If you have the same moon, but you are drawing the free body diagram by sitting on the moon itself. You don't actually have to go to the moon, you have to become an astronaut. But if you imagine that you are an observer on the moon and you want to draw its free body diagram, then how will it look like? You know that there is an earth, you can see the earth, the beautiful blue marble. And you know that there is a gravitational force that the earth is pulling you with. But you again don't see an acceleration just like the person on the lift. So, you ask the person on the lift, what did you do when Newton's law is going to work for you? And he tells you that what I did was I applied a fake force in the direction opposite to the acceleration. So, I applied a fake pseudo force in the direction opposite to the acceleration and its magnitude was ma. And that gave me the correct answer. So, you think to yourself, why don't I do that as well? So, you also apply a fake, completely not real force in a direction opposite to the acceleration. The acceleration was towards the earth. So, you apply a fake force opposite to the earth. And the magnitude is m into A again, m into the centrifugal acceleration which is m v square by r. So, this is also a pseudo force, a fake force, just like before. But in the case of circular motion, we have given a name to this force which is called centrifugal force. It's very unfortunate because it causes a lot of confusion, but it is what it is. So, centrifugal force is nothing but a kind of pseudo force in the case of circular motion. And you can check that again you will get the same equation as G is equal to m v square by r, just like before. But this time, you have drawn the primordial diagram in a non-inertial reference frame, in a frame of reference that is accelerating. So, we cannot forget that. If you simply think of the centrifugal force as an actual force, you might end up thinking that the acceleration of the moon is zero, which is completely not true. We saw that the moon does accelerate. There is an acceleration towards the center of the earth. This is just a way to make Newton's laws work and to get at the correct equation without actually drawing the free body diagram in an inertial frame. All right. So, there is one question left here. We have seen what is centrifugal force. We have also seen when to draw it in a free body diagram when we are accelerating frame. The question that is left is what about that force that we feel inside a car? When we are moving in a car, we feel that force in the outward direction. Why does that happen? Let us finish this video by talking about that force. This is the situation we are talking about. And I have pre-drawn it because I do not draw well as you may have realized. This purple box is supposed to represent the car. This yellow dot represents us and this green arrow represents the direction in which the car is turning. As you can see as the car turns, you go from the center of the car to the right side of the car. We are assuming that you are sitting on a completely frictionless seat. Now, we feel that this turning, this going from the center to the right side of the car is because of the centrifugal force. But no, it is actually simply explained by inertia. See, you want to stay in a straight line path because there is no force acting on you. You are on a frictionless seat, but the car is turning. So, you feel that you are going towards the right of the car because of the force. But you actually just want to stay in your straight line path. In a normal car where there is friction on the seat, you want to stay in the straight line path but friction prevents you. Friction pulls you in this direction and prevents you from going towards the right and keeps you at the center of the car. It makes sure you are at the center of the car. Which is why you feel like you are being pushed out, but it is actually simply inertia. So, this is the real reason for what feels like the centrifugal force. I hope this is clear. Let me summarize the points that we made in this video. We talked about a lot of things. We saw that centrifugal force is not a real force that is actually cancelled by the centripetal force. Centrifugal force actually arises because of being in a non-inertial plane. To understand what is a non-inertial plane, we took the example of a block inside a lift. We saw that if we draw the free body diagram from an inertial frame, a frame where we are not accelerating, we get the correct answer using Newton's laws. But if we do the same thing, if we apply Newton's laws in a non-inertial frame or in an accelerating plane, we do not get the correct answer. So, pseudo forces are just a way to forcefully apply Newton's laws where we put a force in a direction opposite to the acceleration and having magnitude m8. In the case of circular motion, doing this gives us what we call the centrifugal force even though there is no such force actually there. And finally, we talked about why we feel that force when we are driving in a car. We feel that force because of inertia. Our body wants to continue in a straight line motion but the car is turning. So, this means that in the frame of reference of the car, our body wants to go out but the friction in the car keeps us in.