Rotational Motion

Rigid Body
A Rigid body is defined as a body whose particles move in the same way as the body moves.

Rotational Motion
Rotational Motion is the motion of a body which rotates about its own axis. The body performs rotational motion while, the individual particles perform circular motion. The axis of rotation about the centre of mass of a body, is called as its natural axis.

Moment of Inertia
Moment of Inertia of a body is defined as the product of Mass and the square of radius of gyration.

I = MR2

I = MK2

Radius of Gyration
Radius of Gyration is defined as the distance of the axis from its natural axis.

K = sqrt (I/m)

Kinetic Energy of a Rotating Body
Kinetic Energy = Iω2

Torque
Torque = Iα

Rolling Motion
(Rings, Cylinders & Spheres for JEE)

Kinetic Energy = 1/2 MV2 [1+K2/R2]

Velocity = sqrt {2gh / [1+K2/R2]}

Acceleration = gsinθ / [1+K2/R2]

Theorem of Parallel and Perpendicular Axes
Ip = Ic + Mh2

Iz = Ix + Iy

Tips and Tricks

 * 1) For a system of bodies, add up their individual momnts of inertia.