Frame of Reference

Frame of Reference:

Rest and motion are relative terms. To define motion, the observer must define a frame of reference relative to which the motion is considered.

A body in motion can be located with reference to some coordinate system called the frame of reference. If the coordinates of all the points of a body remain unchanged with time and with respect to the frame of reference, the body is said to be at rest. If, however, the coordinates of any point of the body change with time and with respect to the frame of reference, the body is said to be in motion.

Suppose a body P is at the point A. Its coordinates are (x, y, z) with respect to the frame of reference as shown in the above figure. If the body P always remains at A, it will be at rest with respect to the frame of reference. If another body Q is initially at A and after some time it is at B (x₁, y₁, z₁), it is in motion with respect to the frame reference.

Now consider two frames of reference XYZ and X’Y’Z’ as shown below.

The observer O considers the motion of P with respect to the frame of reference XYZ and the observer O’ with respect to the frame of reference X’Y’Z’.

If O and O’ are at rest with respect to each other, they will observe the same motion of P. If O and O’ are in relative motion, their observation of motion will be different.

Examples:

(1) Consider two observers A and B. A is on Earth and B is on the sun. Both observe the motion of the moon. To the observer A, monn will appear to move along a circular path. To the observer B, the moon will appear to move in a wavy path.

(2) Consider a car in motion. To an observer at the centre of the wheel, any point on the rim will appear to move along a circular path. But, to an observer on the ground, the path of the point on the rim will appear to be a cycloid as shown below.

(3) Consider that a train is moving with uniform velocity. A person sitting on the train drops a stone from the window. To this person, the stone will appear to be falling vertically downwards. But, to a person standing near the track, the stone will appear to move along a parabolic path.

(4) Consider a person A sitting in a train. All the windows of the train are closed and the person A cannot see anything outside. If the train is moving with uniform velocity, a stone thrown upward will return to the thrower. It means that this person cannot find the velocity of the train i.e., the frame in which he is located. On the other hand, if the train is accelerated the stone thrown upward will not return to the thrower. This is the case of a non-inertial frame of reference.