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Forces of inertia are real forces, we meet them in our everyday life. At the same time the forces of inertia differ from all other forces because they are not the result of the action of one body on another like a force of gravity, force of tension, force of friction, etc. Forces of inertia result from the properties of the accelerated frame of reference itself. In a frame in which Newton’s description of motion is valid, the force of inertia does notsimply exist.
Summarizing the above speculations we may say:
1.Forces of inertia exist in only non-inertial frames of reference. They do not exist in inertial frames of reference, where any force is understood only in Newton’s description, i.e. as a measure of interaction of objects.
2. As the forces of inertia are not the result of interaction of objects, the 3rd Newton’s law is not applicable to them. This is the reason of calling them fictitious forces sometimes.
3. The magnitude of the force of inertia is proportional to the mass of the object, 
. This proportionality is a common feature of the force of inertia and other forces, the gravitational force among them.
Fig. 1.25
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Imagine ourselves in a laboratory without windows and with its doors closed so that we cannot observe what is outdoors. We even don’t know if the laboratory is on the ground or in the outer space. We make a simple experiment: we take a ball and let it fall. We observe this ball falling with the acceleration 
. It happens if the laboratory is at rest on the ground. Fig. 1.25. (a). But it also happens if the laboratory moves in the outer space with acceleration 
. In this case the force of inertia 
acts on the ball, and it falls on the floor of the laboratory, Fig. 1.25 (b).
Thus, the experiments on free fall cannot help to distinguish between the force of gravity and the force of inertia. Einstein suggested that no physical experiments can distinguish between these two forces. This is the main idea of the Principle of Equivalence of force of gravity and force of inertia, or in other words the idea of the equivalence of gravitational and inertial mass. This remarkable equivalence is the core of Einstein’s General Theory of Relativity.
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