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posted by  mzT on 6/18/2008 12:45:12 PM  |  status: Live  

Acceleration of a Pulley

Course Textbook Chapter Problem
General Physics College Physics (8th) by Young N/A N/A
Question Details:
A string is wrapped around a uniform solid cylinder of radius r, as shown in the figure... The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m. Note that the positive y direction is downward and counterclockwise torques are positive.
 
Find the magnitude alpha of the angular acceleration of the cylinder as the block descends.
Express your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.
 
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posted by booboo123 on 6/18/2008 1:24:59 PM  |  status: Live
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mzT's comment:
"great!"
Response Details:
Forces on block:
mg  - T  =  ma
 
torques on pulley:
Tr  = I α
I = (1/2) m r2     
and a = αr   
so
T  = mg  -  mαr   (first equation... plug into the other)
( mg - mαr) r  = (1/2) m r2 α
 eliminate m from every term, divide by r2
 g/r   -   α   =  (1/2) α 
 g / r   =  (3/2) α
 α  =  2 g / 3r


*cr to MM
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