which is a faster process pure rolling/ pure sliding /rolling for some time and then sliding?

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A bowling ball is thrown down the alley in such a way that it slides with a speed $v_{0}$ initially without rolling. What will it it's speed be when (and if) it starts pure rolling? The transition from pure sliding to pure rolling is gradual, so that both sliding and rolling takes place during this interval.

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Q. When a rolling body moves along an inclined plane, frictional force acts at the point of contact so as to either prevent the relative sliding or oppose the relative sliding. In the case of a rolling body when projected up or down along the inclined plane or spun with some angular speed and kept on the inclined plane, kinetic force of friction comes into play. If we release the body from rest and the angle of inclination

θ (θ_{0})

where

θ_{0}

= minimum angle for which pure rolling can be established, static force of friction comes into play. For instance, let the body (a solid uniform m sphere of mass m, say) be spun with

ω_{0} ↓

and kept on the inclined plane.
The minimum coefficient of friction for which the sphere will have pure rolling after some time for

θ = 45^{\circ}

is :

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