A Brief Review of Newton's Laws of Motion
Let's review certain basic concepts of motion, namely Newton's first two Laws of Motion, which are presumably as basic and fundamental as any natural law can be:
(1) The Law of Inertia: A body which has no force acting on it will move with uniform motion (that is, with constant speed and direction).
(2) The Force Law: If a force acts on a body, it will not move uniformly, but will be accelerated in the direction of the force at a rate proportional to the force, and inversely proportional to its inertia, or mass.
Now, these two laws seem very simple and obvious, and perfectly reasonable and correct. So much so, that if we see an object which is moving uniformly, we presume that it must not have any force (or at least, any net force) acting on it; whereas if we see an object which is accelerating, we presume it must have some force acting on it, in the direction of its acceleration. The strange thing is, that it is not only very easy, but actually more normal than not, for Newton's Laws of Motion to be wrong. For we often find ourselves in a situation in which bodies appear to be accelerating under the influence of some force, even though no such force is actually acting on them.
Inertial Frames of Reference
To understand how such a statement could possibly be true, we need to discuss frames of reference. A frame of reference is simply that portion of the world around us, which we use to measure the motion of moving bodies. For all practical purposes, the world around us appears to be at rest, and insofar as that statement is true, then any motion we measure relative to our surroundings is correctly observed, and if a motion appears uniform, it must truly be uniform, and if the motion appears nonuniform, then it must truly be nonuniform.
But suppose that instead of using the world around us, we use some particular portion of the world, such as a railway car, which is moving...