# Inertial Mass

## Inertial Mass

Newton’s first law of motion states that an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Objects tend to keep on doing what they are doing. In fact, it is the natural tendency of objects to resist changes in their state of motion. This tendency to resist changes in their state of motion is described as inertia. It is the resistance an object has to a change in its state of motion.

Inertial mass is the mass of the material of the body which measures its inertia. If an external force F acts on a body of mass $${{m}_{i}}$$ then according to Newton’s law of motion: $$F={{m}_{i}}a\Rightarrow {{m}_{i}}=\frac{F}{a}$$

Hence, internal mass of a body may be measured as the ratio of the magnitude of the external force applied on it to the magnitude of acceleration produced in its motion.

1) It is the measure of ability of the body to oppose the production of acceleration in its motion by an external force.

2) Gravity has no effect on inertial mass of the body.

3) It is proportional to the quantity of matter contained in the body.

4) It is independent of size, shape and state of body.

5) It does not depend on the temperature the body.

6) It is conserved when two bodies combine physically (or) chemically.

7) When a body moves with velocity$$\left( v \right)$$, its inertial mass is given by:

$$m=\frac{{{m}_{0}}}{\sqrt{1-\frac{{{v}^{2}}}{{{c}^{2}}}}}$$,

Where,

$${{m}_{0}}=$$ Rest mass of body

$$c=$$Velocity of light in vacuum