Chapter 12, Problem 29A

Any rolling object takes more time to roll down an inclined plane than a non-rolling object sliding without friction. Jim says this is because all the PE of the non-rolling object goes into translational KE, with none 'wasted' as rotational KE. John doesn’t think a sliding object slides down an incline faster than a rolling object. With whom do you agree?

To determine

To identify: Whether any rolling object take more time to roll down an inclined plane or a non-rolling object sliding without friction.

Answer to Problem 29A

Agree with J, a rolling object would take the longer time roll down an inclined plane compared to a non-rolling object sliding down without friction.

Explanation of Solution

Introduction:

An object in curvilinear shape converts potential energy into translational and rotational kinetic energy which helps in rolling faster.

When a rolling object rolls down an incline then rotational kinetic energy and translational kinetic energy increase the momentum of the object. Because the rotational kinetic energy will help rolling objects to roll down and translational energy will help it move linearly down an incline. But, friction will also act upon the rolling object which decreases its motion.

In the case of a non-rolling object, when moves linearly down an incline without friction then there is no resistance opposing its motion. Thus, all its potential energy goes into translational kinetic energy only.

Conclusion:

Thus, a non-rolling object will slide down an incline faster than a rolling object without friction rolls down.