# Two Rotational Dynamics Problem

1) 10. Four objects are placed at rest at the top of an inclined plane and allowed to roll without slipping to the bottom in the absence of rolling resistance and air resistance.
• Object A is a solid brass ball of diameter d.
• Object B is a solid brass ball of diameter 2d.
• Object C is a hollow brass sphere of diameter d.
• Object D is a solid aluminum ball of diameter d. (Aluminum is less dense than brass.)
The balls are placed so that their centers of mass all travel the same distance. In each case, the time of motion T
is measured. Which of the following statements is correct?
(A) TB > TC > TA = TD
(B) TA = TB = TC > TD
(C) TB > TA = TC = TD
(D) TC > TA = TB = TD (correct answer)
(E) TA = TB = TC = TD

2) The apparatus in the diagram consists of a solid cylinder of radius 1 cm attached at the center to two disks of radius 2 cm. It is placed on a surface where it can roll, but will not slip. A thread is wound around the central cylinder. When the thread is pulled at the angle θ = 90 to the horizontal (directly up), the apparatus rolls to the right. Which below is the largest value of θ for which it will not roll to the right when pulling on the thread?

To see the diagram for the second problem: