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. 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?

Answer 1

T = string force up
m g = weight force down
m a = mg - T

(I guess the string is wound around the outside of this yo yo)
Torque = I alpha
T R = .5 m R^2 alpha
but alpha = a/R
so T = .5 m a

so
ma = T - .5 ma
(3/2) m a = (1/2) m g
a = g/3
T = .5 m a = (1/2)m g/3
T = mg/6

Answer 2

check my arithmetic
yes, no side force so no side motion

Answer 3

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