Chapter 8.2, Problem 37SSC

To determine

To Explain:The rotation and sliding of a ball on tilted surface with using free-body diagram.

Explanation of Solution

If surface is low friction

i.e. $f=0$

Then only force on ball is $mg\sin \theta$ at center which will give linear acceleration.

If friction is high, then torque acts on ball $fR$ which tries to rotate the ball with angular acceleration $\alpha$ as shown. And at some point of time, velocity and ball of point A be zero and ball will roll.

Conclusion:

If friction is high then torque acts on ball $fR$ which tries to rotates the ball with angular acceleration $\alpha$ as shown. And at some point of time velocity and ball of point A be zero and ball will roll.