The valise is standing in the baggage rack. At the same time, it is moving together with the train. The house is standing on the Earth, but it is also moving together with it. It is possible to say about one and the same body: it is moving in a straight line, it is at rest, it is rotating. And all these statements will be true, but from different points of view.

Not only the graph of the motion but also its properties can be entirely different if regarded from different points of view.

Recall what happens to objects on a ship which is being rocked by the sea. How they misbehave! The ash-tray on the table overturned and dove headlong under the bed. The water splashes in the bottle, and the lamp vibrates like a pendulum. Without any visible cause, some objects begin moving and others stop. An observer on such a ship might say that the basic law of motion is that at any moment an unfastened object can start travelling in any direction with an arbitrary speed.

This example shows that among the various points of view on motion there are those which are really awkward.

But what point of view is the most “reasonable”?

If suddenly, for no reason whatsoever, the lamp on the table were to bend over, or the paper-weight were to jump, then at first you would think that it was only your imagination, If these miracles were repeated, you would urgently start looking for the cause which drove these bodies out of the state of rest.

It is therefore perfectly natural to regard the point of view on motion, according to which bodies at rest do not budge without the action of a force, as a rational one. Such a point of view seems quite natural: a body is at rest—hence, the sum of the forces acting on it is equal to zero; it moved—this happened under the action of a force.

This point of view presupposes the presence of an observer. However, it is not the observer himself who is of interest to us, but his location. Therefore, instead of “point of view on motion”, we shall say “frame of reference in which the motion is regarded”, or simply “frame of reference”.

For us, inhabitants of the Earth, an important frame of reference is the Earth. However, bodies moving on the Earth, say, a ship or a train, can also frequently serve as frames of reference.

Let us now return to the “point of view” on motion which we called rational. This frame of reference has a name—it is called inertial.

We shall see a bit later where this term comes from.

Consequently, the properties of an inertial frame of reference are as follows: bodies in a state of rest with respect to such a frame of reference do not feel the action of forces. Therefore, not a single motion in such a frame of reference is begun without the action of a force. The simplicity and convenience of such a frame of reference are obvious. It would pay to study motion in them.

The fact that the frame of reference associated with the Earth does not differ greatly from an inertial one is extremely important. We can therefore begin our investigation of the basic regularities of motion considering them from the point of view of the Earth. Nevertheless, we must bear in mind that, strictly speaking, everything that will be said in the next section deals with an inertial frame of reference.