Moment of Inertia of Mass

Moment of Inertia of Mass 

• The moment of inertia of a mass about an axis is defined as the product of its mass and the square of its perpendicular distance from the axis.

• If m is the mass of a particle at distance r from an axis AB as shown in Fig. 7.2.1, the moment of inertia is

IAB = mr2

• The moment of inertia of any rigid body can be obtained by finding the moment of inertia of a suitable differential element and then integrating it.

• For a differential element dm of a body shown in Fig. 7.2.2,

• If the body is made up of a material of uniform density ρ,

• Although triple integration is involved in the above equation, the mass moment of inertia can be obtained using only single integration by choosing suitable disc or shell elements and using the relation between mass moment of inertia and area moment of inertia for thin plates which is derived in the next section.

• The distance from the axis at which the whole mass of the body can be considered to be concentrated so as to keep the moment of inertia unchanged is known as the radius of gyration.

If K = Radius of gyration

The S.I. unit of moment of inertia is kg m2.