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December 20, 2014

December 20, 2014

Posted by **Gabe** on Friday, January 22, 2010 at 3:17am.

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.

- physics -
**drwls**, Friday, January 22, 2010 at 6:57amLet T be the string tension. That and the angular acceleration alpha are the unknowns. Separate equations for the acceleration of the block and the angular acceleration of the cylinder will allow you to solve for both variables. The moment of inertia of the cylinder in (1/2) M r^2

m g - T = m a

T*r = torque = I*alpha = (1/2) m r^2 * alpha

T = (1/2) m*r*alpha

m g = ma + (1/2) m r * alpha

= ma + (1/2) m a

(since alpha = a/r)

a = (2/3) g

alpha = (2/3)(g/r)

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