Question

Define moment of Inertia. On what factors does it depend? Derive the expression for the moment of inertia of a rigid body.

Answer 1

The rotational inertia of a body is called its moment of inertia denoted by I. The Moment of inertia depends on: 

1. The size and shape of the body. 

2. The axis of rotation. 

3. The distribution of mass about the axis. The moment of inertia of a body about a given axis is the sum of the products of the masses of each particles and squares of their perpendicular distances from the axis of rotation

Let m₁, m₂, m₃ ………….. are the masses of the particles of the body situated at distance r₁, r₂, r₃ …………… from the axis of rotation then,

I = m₁r₁² + m2r₂² + m₃r₃² + ………

I = Σ mr².