The moment of inertia of a solid cylinder of mass 'm', radius 'R' and length 'l' about the longitudinal axis or polar axis is-

Explanation

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 . Moment of inertia of a particle is I = mr 2 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 = m 1r 12 + m 2r 22 + m 3r 32 + m 4r 42 + ------- The moment of inertia of a solid cylinder of mass 'M' and radius 'R' about the axis of the cylinder Important Points Body Axis of Rotation Moment of inertia Uniform circular ring of radius R perpendicular to its plane and through the center MR 2 Uniform circular ring of radius R diameter Uniform circular disc of radius R perpendicular to its plane and through the center Uniform circular disc of radius R diameter A solid sphere of radius R diameter A hollow sphere of radius R diameter A hollow cylinder of radius R Axis of cylinder MR 2 ⇒I = ​ 2 MR2 ​ 2 MR2 ​ 2 MR2 ​ 4 MR2 ​MR 5 2 2 ​MR 3 2 2