A yo-yo with mass M and radius R is wound with a light string. Someone drops it from rest with the string attached to a metal pole. The yo-yo falls and unwinds (spins) without slipping. The moment of inertia for the yo-yo is ½ MR^2 (a disk).

Question

A yo-yo with mass M and radius R is wound with a light string.  Someone drops it from rest with the string attached to a metal pole.  The yo-yo falls and unwinds (spins) without slipping.  The moment of inertia for the yo-yo is ½ MR^2 (a disk).

a. In terms of g, find the downward acceleration of the center of mass of the yo-yo as it unrolls from the string.

b. What is the tension in the string as the disk unwinds and falls?

c.While descending, does the center of mass of the yo-yo move to the left, the right, or straight down?  Explain your answer in complete sentences.

I think straight down, but why?