Moment of Inertia

Moment of Inertia Formula
The Moment of inertia is the property by the virtue of which the body resists angular acceleration. In simple words we can say it is the measure of the amount of moment given to the body to overcome its own inertia.
It’s all about the body offering resistance to speed up or slow down its own motion.
Moment of inertia is given by the formula

Where
R = Distance between the axis and rotation in m
M = Mass of the object in Kg.
Hence the Moment of Inertia is given in Kgm2.

Moment of Inertia Formula helps to calculate the moment of inertia of the given body. It depends on the shape and mass distribution of the body and on the orientation of the rotational axis.

Moment of Inertia Problems

Below are given problems based on moment of inertia which helps you to understand where we can use these formulas.

Question 1: Calculate the Moment of inertia of the ball having mass of 5 Kg and radius of 3 cm?
Solution:

Given: Mass of the ball = 5Kg,
Radius of the ball = 3 cm = 0.03 m,
Moment of Inertia is given by I = MR2 = 5 Kg × (0.03 m)2 = 0.0045 Kgm2.

Question 2: A sphere is moving around in air. If the moment of inertia is 10 Kgm2 and radius of 1m, calculate its mass?
Solution:

Moment of inertia I = 10 Kgm2,
Radius of sphere R = 1m,
Moment of Inertia I = MR2
Mass of the body M = IR2 = 10Kgm21 = 10 Kg.