# Friction of a sliding, then rolling, sphere

The motion of a sphere moving on a rough horizontal surface changes from pure sliding to pure rolling. In this process, the force of friction:

(a)initially acts opp to motion and then in direction of motion

(b)causes linear retardation

(c) causes angular acceleration

(d) stops acting acting when pure rolling begins.

This is a multi correct answer type question.

The answer given is (b,c,d). This is what I could think about:

The rolling must require a driving force and that is provided by friction. So friction must be there initially. But for the sphere to rotate and slide, friction must be opposing linear motion. So friction causes linear retardation and angular acceleration. And friction opposes the direction of motion as long as it is acting in this case.

So b,c,d looks fine. But then why doesn't the sphere start rolling as soon as it starts moving?

But then why doesn't the sphere start rolling as soon as it starts moving?

Pure sliding, ie no change in rotation, cannot occur unless there is no friction between the sphere and the horizontal surface at the point of contact.
It might be that the frictional force is small so that the torque due to the frictional force is also not large enough to produce a noticeable rotation and a noticeable slowing down of the sphere.

So for an instant of time the sphere might be sliding and not rotation but after that the frictional force will cause the ball to rotate and to slow down with some of the translational kinetic the sphere being converted into rotational kinetic energy and heat.