QP16

At t = 0, a solid sphere of mass M and radius R is spinning backwards while moving forwards on a table top of frictional coefficient µ . The initial velocity of the sphere is v₀ and the initial angular velocity is ₀ = -2v₀ / R as shown below.

 

(2 points)  (a)  At what time t₀ does the sphere first roll without slipping?

(2 points)  (b)  For times t >> t₀, draw and label a similar picture of sphere as above. Indicate the magnitude and direction
                               of both the velocity and angular velocity.

(1 point )  (c)  What is the magnitude and direction of the frictional torque,  _f  , at t = 0? What is it for t >> t₀?