Which of the following statements is correct? a) Consider two identical inclines

Question

Which of the following statements is correct?

a) Consider two identical inclines except the first is frictionless and the second is not. A ball released from rest from the top of the first incline slides down the first incline. A ball released from rest at the top of the second incline rolls without slipping. Because of conservation of energy, a ball released from rest at the top of the first incline would take the same time to reach the bottom as it would take the ball to reach the bottom released from rest at the top of the second incline.

b) A uniform ball that rolls without slipping has rotational kinetic energy equal to its translational kinetic energy.

c) For objects rolling without slipping, the ratio of rotational kinetic energy to translational kinetic energy depends on the distribution of mass but is independent of the total mass.

Explanation / Answer

b) If an object is rolling without slipping, then its kinetic energy can be expressed as the sum of the translational kinetic energy of its center of mass plus the rotational kinetic energy about the center of mass.

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