Rotational motion:
The motion of a rigid body which takes place in such a way that all of its particles move in circles about an axis with a common angular velocity; the rotation of a particle about a fixed point in space. Rotational motion is illustrated by
(1) the fixed speed of the rotation of Earth about its axis;
(2) the varying speed of the rotation of flywheel of a sewing machine;
(3) the rotation of the satellite about the planet;
(4) the motion of an ion in a cyclotron; and
(5) the motion of a pendulum. Circular motion is the rotational motion in which each particle of rotating body moves in the circular path about an axis. Such motion is exhibited by 1st and 2nd examples.
Suppose that you are replacing the bearings in wheel of your bicycle. To test if you have done a good job, hold the axle vertically and give it a spin. The axle at the center of wheel is stationary. The wheel has no translational motion. Such type of motion around an axis of rotation is known as rotational motion .The speed of rotation, or angular velocity, remains constant in the uniform circular motion. In this case, angular displacement θ experienced by particle or rotating body in a time t is θ = ωt, where ω is the constant angular velocity. Rotational motion takes place if every particle in the body moves in the circle about a single line. This line is called as axis of rotation. Then the radius vectors from axis to all the particles undergo the same angular displacement in same time.
The axis of rotation is not required go through the body. A rotating body possesses kinetic energy of rotation which can be expressed as Trot = ½Iω2, here ω is the magnitude of the angular velocity of the rotating body and I is the moment of inertia, which is a measure of the opposition of body to angular acceleration. The moment of inertia of the body depends on the mass of a body and distribution of mass relative to the axis of rotation. For instance, the moment of inertia of a solid cylinder of mass M and radius R about its axis of symmetry as ½MR2.