Newtons' first law of motion is also known as the law of inertia, which states that any object in a state of rest or of uniform linear motion tends to remain in such a state unless acted upon by an unbalanced external force. In effect, this is a definition of equilibrium; the branch of physics that treats equilibrium situations is statics. The tendency for matter to maintain its state of motion is known as inertia. The inertia of a body is its tendency to resist acceleration, or change in its velocity. The mass of a body is a quantitative measure of its inertia. Thus, a very massive object, such as a steamship, requires a significant force acting for considerable time in order to bring it either to a stop or up to speed, whereas a relatively light object, such as a table-tennis ball, requires little effort to change its velocity.
A rotating body has the same tendency to maintain its state of rotational motion that a body moving in a straight line has to maintain its linear motion. The moment of inertia is a measure of a body's resistance to changes in rotation rate. Specifically, torque T and angular accelerationare related through the moment of inertia I by the equation T = I , just as force f and acceleration a are related through the mass m by the equation f = ma. The relationship of the f to the angular acceleration can be seen in graph1. This shows us that there in no relationship between the force of an object and its angular acceleration. Graph2 illustrates the linear relationship between the torque of an object and the angular acceleration. In this graph there is a definite linear equation to produce an ideal relation.
The moment of inertia depends not only on the mass of the body but also on the distribution of mass relative to the axis. This distribution accounts for the fact that objects of various shapes with the same masses and diameters (such as sphere, solid cylinder, hollow cylinder, or wheel and axle) will not take the same time to roll down an inclined plane.