Angular Acceleration Homework: Find w/ Radius, Mass

[moondawg]

Homework Statement

A string is wrapped several times around the rim of a small hoop with radius .08m and mass .18kg. The free end of the string is pulled upward in just the right way so that the hoop doesn't move vertically as the string unwinds. Find the angular acceleration of the hoop as the string unwinds.

Homework Equations

The Attempt at a Solution

So at first i thought i would use 2 equations of torque to find the ang accel(I$$\alpha$$=Fd) but that didnt give me the correct answer in the back of the book of 123 rad/sec². So my friend helped me out and said to set radius x mass equal to MR²$$\alpha$$. and that did give me the correct answer i just don't see the logic in setting those 2 equal to each other bc why would r x m be on one side of the equation?! Pleassseee help!

 

[cupid.callin]

Find torque

τ = Fd
d is perpendicular distance

and hope you can find moment of inertia of the body

...

then use

τ = Iα