Question

Define moment of inertia. State the factors which it depends on. Obtain its dimensions and state its SI unit. 

OR 

Define moment of inertia. State its dimensions and SI units.

Answer 1

(1) Moment of inertia : The moment of inertia of a body about a given axis of rotation is defined as the sum of the products of the masses of the particles of the body and the squares of their respective distances from the axis of rotation.

If the body is made up of N discrete particles of masses m₁ , m₂ , …,m_N situated at respective distances r₁ , r₂ , …, r_N from the axis of rotation, the moment of inertia of the body is 

For a rigid body, having a continuous and uniform distribution of mass, the moment of inertia is

I = \(fr^2dm\) ....(2)

where dm is the mass of an infinitesimal element, situated at distance r from the axis of rotation.

(2) The moment of inertia of a rigid body depends on 

1. the mass and shape of the body 

2. orientation and position of the rotation axis 

3. distribution of the mass about the rotation axis.

(3) Dimensions : [Moment of inertia] = [mass] [distance]²

= [M] [L²] = [M¹L²T⁰]

(4) SI unit : The kilogram-metre² (kg.m²)