Centre of mass . Motion of centre of mass . Linear momentum of a system of particles . Vector product of two vectors .
Angular velocity and its relation with linear velocity . Torque and angular momentum . Equilibrium of a rigid body . Moment of inertia .
Kinematics of rotational motion about a fixed axis . Dynamics of rotational motion about a fixed axis . Angular momentum in case of rotation about a fixed axis Summary Points to Ponder Exercises block sliding down an inclined plane without any sidewise movement. The block is taken as a rigid body.
Its motion down the plane is such that all the particles of the body are moving together, i.e. they have the same velocity at any instant of time. The rigid body here is in pure translational motion (Fig. .
). In pure translational motion at any instant of time, all particles of the body have the same velocity. Consider now the rolling motion of a solid metallic or wooden cylinder down the same inclined plane (Fig. .
). The rigid body in this problem, namely the cylinder, shifts from the top to the bottom of the inclined plane, and thus, seems to have translational motion. But as Fig. .
shows, all its particles are not moving with the same velocity at any instant. The body, therefore, is not in pure translational motion. Its motion is translational plus ‘something else.’ In order to understand what this ‘something else’ is, let us take a rigid body so constrained that it cannot have translational motion. The most common way to constrain a rigid body so that it does not have translational motion is to fix it along a straight line.
The only possible motion of such a rigid body is rotation . The line or fixed axis about which the body is rotating is its axis of rotation . If you look around, you will come across many examples of rotation about an axis, a ceiling fan, a potter’s wheel, a giant wheel in a fair, a merry-go-round and so on (Fig . (a) and (b)).