Inertial reference frames

Consider a ball on the floor of a train. If the train moves with constant velocity, the ball stays at rest, but if someone pulls the the emergency brake, the ball will start to move forwards.

How could the ball change its state of motion when there was no force to cause it to do so? Is Newton's first law invalid?

No, it is not. The problem here is that the braking train is not a so-called inertial reference frame: viewed from outside the train, the ball retains its state of motion whilst the train accelerates backwards.

(A frame of reference is a reference point with a set of axes – a coordinate system – attached to it.)

Inertial reference frame

An inertial reference frame is a frame of reference in which a body on which no force is acting retains its state of motion.

Newton's laws are only valid in inertial reference frames.

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