Problem
The passenger. You are travelling on a train, seated at a small table; a ball is at rest on the table. The train begins to slow down. From your point of view (on the train) the ball rolls forward. From the point of view of an observer standing still on the ground, what is the ball actually doing? Which of the two “is right”, and in what sense? Discuss with reference to the concept of a reference frame.
Solution
The observer on the ground (inertial frame). Before braking, train, table and ball are all moving together at the same speed. When the train slows down, no appreciable horizontal force acts on the ball (the table is smooth): by the first law it retains its own velocity, continuing in uniform straight-line motion. It is not the ball that accelerates forward: it is the train (and with it the table) that decelerates, “sliding out” from under the ball. Seen from the ground, the ball simply carries on moving straight ahead as before.
The passenger (non-inertial frame). The passenger is fixed relative to the train, which is decelerating: theirs is an accelerated, i.e. non-inertial, reference frame. Relative to them, the ball spontaneously sets off forward, as if pushed by a force. But no body actually exerts this force: it is a fictitious (or apparent) force, which appears only because we are describing the motion from an accelerated frame.
Who is right? Both describe correctly what they see, but only the observer on the ground is in an inertial reference frame, one in which Newton’s laws hold without having to introduce fictitious forces. The passenger, to make the sums work, has to add by hand a forward force that does not actually exist. In this precise sense, the “fundamental” description is that of the inertial observer: the motion of the ball is explained by the principle of inertia alone, with no artifice needed.
Links
Topics: Dynamics Concepts: First law of dynamics