Question

Show that the law of conservation of linear momentum is valid in ALL inertial frame.

Answer 1

Inertial references frames are reference frames in which Newton first law of motion holds i.e. an object at rest and an object in motion remains motion unless acted by a net force. An inertial reference frame is either at rest or moves with a constant velocity.

So, there can be two cases 1. Frame of reference is not moving or 2. moving with a constant velocity.

Note: Accelerated frame of reference excerts a force on the object in opposite direction and linear momentum is not conserved.

Now, if a cricket ball is sitting in a glass elevator that is descending, an outside observer, looking into the elevator, sees the ball moving, so, to that observer, the ball has a non-zero momentum. and to someone inside the elevator, the ball does not move, so, it has zero momentum. The two observers each have a frame of reference, in which, they observe motions, and, if the elevator is descending steadily, they will see behavior that is consistent with those same physical laws.

Thus, momentum is conserved in both reference frames. Moreover, as long as the force has the same form, in both frames, Newton's second law is unchanged. Forces such as gravity, which depend only on the scalar distance between objects, satisfy this criterion.

This is called Newtonian invarience.