(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Ʃτ=rxF=Iα

F=mA

ω_{f}^{2}=ω_{i}^{2}+2αΔθ

3. 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?

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# Final angular velocity of a mass on a pulley

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