- #1
austindubose
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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/s2 for acceleration due to gravity.
Homework Equations
Ʃτ=rxF=Iα
F=mA
ωf2=ωi2+2αΔθ
The Attempt at a Solution
Sum of torques:
Ʃτ=rxf
=(.6m)(3kg*10m/s2)(sin 90°)=Iα
--> 18 kgm2/s2=Iα
α=18/[.5(5)(.62)]
α=20 rad/s2
But plugging this into the kinematic equation to solve for ωf doesn't give me the right answer (I know this because I calculated ωf based on conservation of energy first (ωf=11.01 rad/sec), so I think I may have messed up somewhere up until this point. Any suggestions?