Rotational motion

When a body rotates about a fixed axis, its motion is known as rotatory motion. A rigid body is said to have pure rotational motion, if every particle of the body moves in a circle, the centre of which lies on a straight line called the axis of rotation. The axis of rotation may lie inside the body or even outside the body. The particles lying on the axis of rotation remains stationary. The position of particles moving in a circular path is conveniently described in terms of a radius vector r and its angular displacement θ . Let us consider a rigid body that rotates about a fixed axis XOX' passing through O and perpendicular to the plane of the paper. Let the body rotate from the position A to the position B. The different particles at P1,P2,P3.. in the rigid body covers unequal distances P1P1', P2P2', P3P3'. in the same interval of time. Thus their linear velocities are different. But in the same time interval, they all rotate through the same angle and hence the angular velocity is the same for the all the particles of the rigid body. Thus, in the case of rotational motion, different constituent particles have different linear velocities but all of them have the same angular velocity.

Rotation around a fixed axis is a special case of rotational motion. It does not involve rotation around more than one axis, and cannot describe such phenomena as wobbling or precession. The kinematics and dynamics of rotation around a fixed axis of a rigid object are mathematically much simpler than those for rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion.