Moment of Inertia

Moment of inertia plays the same role in rotational motion as mass plays in linear motion. It is the property of a body due to which it opposes any change in its state of rest or of uniform rotation.

(1) Moment of inertia of a particle I = mr²; where r is the perpendicular distance of particle from rotational axis.

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

I = m₁r₁² + m₂r₂² + m₃r₃² + …………

(3) Moment of inertia of a continuous distribution of mass, treating the element of mass dm at position r as particle

dI = dmr² i.e., I = ∫r²dm

(4) Dimension : [ML²T⁰]

(5) S.I. unit : kgm².

(6) Moment of inertia depends on mass, distribution of mass and on the position of axis of rotation.

(7) Moment of inertia does not depend on angular velocity, angular acceleration, torque, angular momentum and rotational kinetic energy.

Physical Significance of Moment of Inertia

Moment of inertia plays the same role in rotational motion as that of mass in translator motion. Also, to bring about a change in the state of rotation, torque has to be applied.