# 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.
• Moment of inertia of a particle I = mr2, where r is the perpendicular distance of particle from rotational axis.
• Moment of inertia of a body made up of number of particles (discrete distribution),

I = m1r12 + m2r22 + m3r32 + ...
• Moment of inertia of a continuous distribution of mass, treating the element of mass dm at position r as particle,

dI = dmr2, i.e.,
• Moment of inertia depends on mass, distribution of mass, and position of axis of rotation.
• Moment of inertia does not depend on angular velocity, angular acceleration, torque, angular momentum, and rotational kinetic energy.
• It is not a vector as direction (clockwise or anti-clockwise) is not to be specified and also not a scalar as it has different values in different directions. Actually, it is a tensor quantity.
• In case of a hollow and solid body of same mass, radius, and shape for a given axis, moment of inertia of hollow body is greater than that for the solid body because it depends upon the mass distribution.