PURE ROLLING

A rigid body I = CMR^(2) is set into a motion on a rough horizontal surface with a linear speed v_(0) in the forward direction at time t = 0 as shown in figure. After what time slipping finally stop and pure rolling starts. Find the linear speed of the body after it starts pure rolling on the surface.

The motion of a sphere moving on a rough horizontal surface changes from pure sliding (without rolling) to pure rolling (without slipping). In this process, the force of friction ( i ) intially acts opposite to the direction of motion and late in the direction of motion ( ii ) cause linear retardation ( iii ) causes angular acceleration ( iv ) stops acting when pure rolling begins

A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction =mu ) with speed of centre =u . It collides inelastically with a smoothh vertical wall at a certain moment, the coefficient of restituting being (1)/(2) . The sphere will begin pure rolling after a time.

A hollow sphere of radius R and mass m fully filled with water of mass m . It is rolled down a horizontal plane such that its centre of mass moves with a velocity v . If it purely rolls.

In this passage a brief idea is given of the motion of the rolling bodies on an inclined plane. We will consider three cases: objects are released on an incline plane Case-A: which is smooth. Case-B: where friction is insufficient to provide pure rolling. Case-C: where friction is sufficient to provide pure rolling. Force diagram for three cases are as follows: (where symbols have their usual meanings) We have four objects: a solid sphere, a hollow sphere, a ring and a disc, all of same radius. When these are released on an inclined plane, it may happen that all of them do not perform pure rolling. But from the information of pure rolling, if one object can be confirmed to be purely rolling then it can be said that rest all will perform pure rolling. This object whose pure rolling confirms pure rolling of all other objects is

A sphere has to purely roll upwards. At an instant when the velocity of sphere is v, frictional force acting on it is