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## Homework Statement

Use Newton's 2nd Law, sum of torques, and kinematic equations to determine the angular speed of the spool shown in the figure below. Assume the string has a negligible mass, and it turns without slipping. Use g=10 m/s

^{2}for acceleration due to gravity.

## Homework Equations

Ʃτ=rxF=Iα

F=mA

ω

_{f}

^{2}=ω

_{i}

^{2}+2αΔθ

## The Attempt at a Solution

Sum of torques:

Ʃτ=rxf

=(.6m)(3kg*10m/s

^{2})(sin 90°)=Iα

--> 18 kgm

^{2}/s

^{2}=Iα

α=18/[.5(5)(.6

^{2})]

α=20 rad/s

^{2}

But plugging this into the kinematic equation to solve for ω

_{f}doesn't give me the right answer (I know this because I calculated ω

_{f}based on conservation of energy first (ω

_{f}=11.01 rad/sec), so I think I may have messed up somewhere up until this point. Any suggestions?