# What is the formula for Moment of Inertia of a rigid body?

Posted in ROTATIONAL MOTION | Email This Post |Inertia of a body is its inability to change by itself its state of rest or of uniform motion in a straight line. Similarly Moment of inertia of a body is its inability to change by itself its state of rest or of uniform rotatory motion about an axis.

The formula for Moment of Inertia of a rigid body is given as,

The moment of inertia of the rigid body (l) = Sum of moments of inertia of

all the particles present in the body.

Let us consider,

m_{1}, m_{2}, m_{3} = masses of large particles in a rigid body

r_{1}, r_{2}, r_{3} = distance of the masses from the axis

The formula for Moment of Inertia of a rigid body will be,

** l= m _{1}r_{1}^{2} + m_{2}r_{2}^{2} + m_{3}r_{3}^{2} + …**

The above formula can also be expressed as,

** **

m_{i} = mass of i^{th} particle

r_{i} = distance between i^{th }particle and axis o rotation