A solid disc and a solid sphere have the same mass and same radius. Which one has the higher moment of inertia about its centre of mass?

CONCEPT:

Moment of inertia:

• Moment of inertia of a rigid body about a fixed axis is defined as the sum of the product of the masses of the particles constituting the body and the square of their respective distances from the axis of the rotation.
• The moment of inertia of a particle  is

⇒ I = mr2

Where r = the perpendicular distance of the particle from the rotational axis.

• Moment of inertia of a body made up of a number of particles (discrete distribution)

⇒ I = m1r12 + m2r22 + m3r32 + m4r42 + -------

EXPLANATION:

• Moment of inertia of the disc about an axis passing through center and perpendicular to its plane is given by -

\(⇒ {I_{disc}} = \frac{1}{2}M{R^2} = 0.5M{R^2}\)

• Moment of inertia of the solid sphere about an axis passing through center and perpendicular to its plane is given by -

\(⇒ {I_{sphere}} = \frac{2}{5}M{R^2} = 0.4M{R^2}\)

• So, from above it is very clear that the moment of inertia of the disc is greater than the moment of inertia of the solid sphere.