A uniform wheel of radius R is set into rotation about its axis at an angular speed ω. This rotating wheel is now placed on a rough horizontal surface with its axis horizontal. Because of friction at the contact, the wheel accelerates forward and its rotation decelerates till the wheel starts pure rolling on the surface. Find the linear speed of the wheel after it starts pure rolling.
Given:
Radius of wheel= R
Angular speed= 
When it is placed on the rough surface, due to friction of the surface, its acceleration decreases.
We consider the point A where external torque is zero. Using the law of conservation of angular momentum. Before rolling and after rolling, the angular momentum remains constant.
Therefore, angular momentum=
After pure rolling the velocity of the wheel let v
Hence, angular momentum= 
=
Equating equation (1) and (2)
