 When do we say that a body is at rest and when do we say it is in motion? We can say that if a body does not change its position, that is where the object of the body is at any particular time, if a body does not change its position as time passes, it is at rest. And if a body does change its position with time, we can say that it is moving. So for example, a fruit on a table remains on the table and we say that it is at rest. But if someone is watching this setup from let's say from the moon, then the whole earth is changing its position. And so the fruit and the table, everything is changing its position. The fruit is at rest if it is viewed from the room itself, from the very room that the table and the fruit is kept in. But it is moving if it is viewed from the moon. It entirely depends on where the viewer is, where are you watching the fruit from. So there is no meaning to the word rest or motion without the viewer. And with the fruit on the table example, we saw that nothing is in an absolute state of rest or in an absolute state of motion. The moon moves with respect to the earth and so with respect to the fruit on the table. And the fruit on the table moves with respect to the moon. But both the fruit and the table are at a state of rest with respect to someone standing in the very room that the table is kept in. So nothing is absolutely moving or absolutely at a state of rest. It all depends on where the viewer is. According to the viewer's position, things can seem to be in a state of rest or things can seem to be in a state of motion. Let's take another example. So here we have two passengers in a tray which is moving to the right and the passengers are at rest with respect to each other. They are just sitting in front of each other and they know they are not moving. They are looking at the person in front of them. According to their reference, the other person is at a state of rest. They are not moving. But they are moving with respect to someone on the platform. They are moving with respect to someone standing on the platform. And they are moving with a speed of whatever their speed of the train is. Let's say this is 80 km per hour. So both the passengers are moving. They are in a state of motion with a speed of 80 km per hour with respect to the person standing on the platform. So any measurement of position, distance or speed, it must be made with respect to a reference frame. In this case, the fruit and the table, they are moving with some speed with respect to the reference frame, some reference frame on the moon. But they are in a state of rest with respect to a reference frame that is in the room, in the very room that the table is kept in or on earth. So a frame of reference really is a set of axis from which the position and motion of an object are described. And we can set mutually perpendicular. We can set perpendicular axis at a perpendicular to each other that are mutually perpendicular and name them x, y and z axis like this. This could be a y axis, x axis and a z axis. And the coordinates x1, y1, z1 of the particle then specify the position of the particle with respect to this frame. We can add a clock to measure the time into this frame of reference. So if these three coordinates, if they remain unchanged as time passes, as this time keeps on passing, if these coordinates do not change, then we can say that the particle is at rest with respect to this frame. But if anyone or all of them or two of them, if any coordinate change with time, somewhat like this, if any coordinate change with time, then we say that the body is moving with respect to this frame. And there is no rule or restriction really on the choice of a frame. You might be thinking which frame do we choose? Do we choose the frame that we are in from our frame or do we choose some frame that is attached to some any other object? There is no rule really. As long as one mentions a velocity with which something is moving with respect to a particular frame, things are clear. So for example, if let's come back to this train example, we can choose a frame of reference according to our convenience to describe the situation. So let's say there is this passenger in the train who is walking in this direction. Let's say with a speed of, with some speed of, we could call it five kilometers per hour. Then this passenger speed with respect to a frame of reference in the train, somewhat like this, let's say there are a set of axes which is attached to this train's compartment, then this person's speed would be five kilometers per hour with respect to the train frame, the frame of reference of the train. Or we can say that these two passengers, they will say that this person is moving with a speed of five kilometers per hour with respect to their own frame of reference, which is the train's frame of reference. But what will this person on the platform say about the person's motion? Well, this person could say that the person is moving, this person is moving with a speed of 85, this train speed 80 and the person's own speed five kilometers per hour. So moving with a speed of 85 kilometers per hour with respect to my own frame of reference, which is maybe the platform's frame of reference. So these two passengers, they will say that we are at a state of rest. But this one is moving with a speed of five kilometers per hour and the person on the platform is moving with a speed of 80 away from us for the speed of 80 kilometers per hour away from us. That is how these two passengers would describe the situation around them. Because their frame of reference are these red set of axes, the train's frame of reference. But this person, this person will say that all three of them are actually moving because I am looking at the things from my own frame of reference, from the platform's frame of reference, which according to me is at rest and you all are moving and you are moving at a speed of 85 and you both are moving at a speed of 80. In almost all the cases, at least in this unit in this chapter and in the coming chapters, we will assume that the frame of reference is already chosen and we are describing the object's motion from that frame of reference. So for example, if a train is moving and a car is not moving, then both of their motions are described from the frame of reference of the road on which we are standing and looking at these two objects. And we will mostly talk about alternate frames of reference, that is frame of reference of the train or the car later, later down in the course. Now in physics, in physics we can categorize, we can categorize motion into three types. There is, there is translational motion. There is rotational motion and there is vibrational. A train moving in a straight line is an example of a translational motion. And Earth spinning on its axis is a case of rotational motion. For vibrational motion, we can think about pendulums. Pendulums can swing from one position to a different position. This is a case of vibrational motion. The back and forth movement of a pendulum is vibrational. In this chapter and in the coming few chapters, we will only focus on translational motion. So even if, even if an object, such as this cricket ball, even if it can rotate like this, we will still sort of ignore, we will ignore the rotational part of it. We will only focus on its translational motion, its motion along a straight line. And as we learn about, as we learn to describe these translational motions, we will assume that the object is a point object. We will assume that the object is a point, a point object. A point object is an object with negligible, almost infinitely small dimensions. Or we can say with almost no dimensions, it's just assumed as a point. For example, if you want to describe the motion of the moon around the Earth, then we can consider both of them as point, as point objects. And can get a good amount of data to be able to describe their motion without much error. And this approximation makes sense because the distance between the moon and the Earth is so large compared to the radius of the moon that we can assume the moon as a point object. Even the radius of the Earth is nothing compared to the distance between the Earth and the moon. Similarly, if this train, let's say this train is moving from New Delhi to Mumbai, then we can assume the train to be as a point object. Because the distance between those two cities, which is around 1250 kilometers, 1, 2, 5, 0 kilometers, that distance is so large compared to the length of the train. We can assume the train to be as a point object. And we can get a good amount of reasonable amount of accurate data without any sort of error when we are describing the train's motion. So in a good number of situations in real life, the size of the objects can be neglected and they can be represented as point objects.