Rolling motion

Rolling motion:

Objects like a cylinder, sphere, wheels, etc. are quite often seen to perform rolling motion. In the case of pure rolling, two motions are undertaking simultaneously; circular motion and linear motion. Individual motion of the particles is too difficult to describe. So, for theory considerations we can consider the actual motion to be the result of:

(i) rotational motion of the body as a whole, about its own symmetric axis and

(ii) linear motion of the body assuming it to be concentrated at its centre of mass.

In other words, the centre of mass performs purely translational motion. 

Accordingly, the object possesses two types of kinetic energies, rotational and translational. Sum of these two is its total kinetic energy. Consider an object of moment of inertia I, rolling uniformly. Following quantities can be related. 

Static friction is essential for a purely rolling motion as it prevents sliding. You might have noticed that many a times while rolling down, the motion is initially a purely rolling motion that later on turns out to be a sliding motion. Similarly, if you push a sphere-like object along a horizontal surface, initially it slips for some distance and then starts rolling. 

Linear Acceleration and Speed While Pure Rolling Down an Inclined Plane: Figure shows a rigid object of mass M and radius R, rolling down an inclined plane, without slipping. Inclination of the plane with the horizontal is θ. As the objects starts rolling down, its gravitational P.E. is converted into K.E. of rolling. Starting from rest, let v be the speed of the centre of mass as the object comes down through a vertical distance h.