1. Show all your work for each part of the question. The parts within the question may not have equal weight.
Figure 1 Figure 2
A person is standing on a horizontal disk-shaped platform that can rotate with negligible friction about an axis at the disk's center. Initially, as shown in Figure 1, the person is standing at the center of the disk as the disk rotates in the counterclockwise direction with a constant angular speed ?i. Then, as shown in Figure 2, the person walks to the edge of the rotating disk. When the person reaches the edge, the disk rotates counterclockwise with a constant angular speed ?f.
The mass of the person is mp, and the mass and radius of the disk are mD and R, respectively.
(a) Indicate whether ?f is greater than, less than, or equal to ?i.
___ ?f > ?i ___ ?f < ?i ___ ?f = ?i
Justify your answer using physics principles, without deriving or manipulating equations.
The rotational inertia of the disk about its center is 1/2 mD R^2.
(b) Derive an equation for ?f in terms of ?i, mp, mD, R, and physical constants, as appropriate.
(c) Indicate whether the equation derived in part (b) is consistent with the claim you selected in part (a). Justify your answer.
