A 42-lb sphere with radius R = 4 in is placed on a horizontal surface with initial angular...

A 42-lb sphere with radius R = 4 in is placed on a horizontal surface with initial angular velocity ω0 = 40 rad/s. The coefficient of kinetic friction between the sphere and the surface is μk= 0.06. What maximum velocity will the center of the sphere attain, and how long does it take to reach that velocity?

Strategy: The friction force exerted on the spinning sphere by the surface will cause the sphere to accelerate to the right. The friction force will also cause the sphere’s angular velocity to decrease. The center of the sphere will accelerate until the sphere is rolling on the surface instead of slipping relative to it. Use the relation between the velocity of the center and the angular velocity of the sphere when it is rolling to determine when the sphere begins rolling.