Bowling Ball Slipping and Rolling: Analyzing Acceleration

[jnimagine]

A uniform, spherical bowling ball of mass m and radius R is projected horizontally along the
floor at an initial velocity v0 = 6.00 m/s. The ball is not rotating initially, so w0 = 0. It
picks up rotation due to (kinetic) friction as it initially slips along the floor. The coefficient of
kinetic friction between the ball and the floor is μk. After a time ts, the ball stops slipping and makes a transition to rolling without slipping at angular speed ws and translational velocity _s. Thereafter, it rolls without slipping at constant velocity.

(b) Find an equation for the linear acceleration a of the ball during this time. The acceleration should be negative, since the ball is slowing down.
(c) Find an equation for the angular acceleration a of the ball while it is slipping. It will be
simpler if you use the sign convention that clockwise rotations are positive, so  > 0.
(d) What constraint on w and v must take effect at time t = ts, the moment when the ball
stops slipping and begins rolling without slipping?

Here is my attempt:
b) slipping = rw + deltavt = vt
and then you get a derivative of it to get a = u_kg
c) a = torque / I
r(ru_kmg / 2/5mr^2) + dv/dt = -u_kg
and we get like -7/2u_kg from this...
d)...

please help!

 

[Doc Al]

Friction is the only horizontal force acting on the ball. Use Newton's 2nd law for translation and rotation to find the linear and angular accelerations.

For (d), what's the condition for rolling without slipping?