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We call systems which obey the
principle of inertia inertial reference
systems: for a body to accelerate it must
be subjected to an outside force. In these systems Newton's other two
laws of motion also apply by extension.
The figure below represents a train travelling at a constant velocity.
There is a box inside it.
The movement of the box is described for each observer O and O' in a
different manner. As both reference systems are inertial, it is not
necessary to refer to any outside force to explain the movement of the
box.
If the box accelerates it is because there is a force acting on it; if
it does not accelerate, there is no force acting on it.
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