Angular acceleration of cylinder with hanging block on string

[jaded18]

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.
http://session.masteringphysics.com/problemAsset/1011172/10/MAD_ia_6.jpg
Find the magnitude alpha of the angular acceleration of the cylinder as the block descends.

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I know that F=ma = -(T-mg) and
magnitude of torque that acts on pulley = I(alpha) = -Tr
and -T = 1/2 (m*r*alpha) if we substitute (0.5m(r^2)) which is the moment of inertia of a uniform cylinder in the second equation
and I also know that a = -alpha (r)

I guess I just don't see how i can use system of equations to eliminate T and still get an answer with variables r and g in the end ..

 

[learningphysics]

All you need to do is solve your equations...

ma = -(T-mg) (1)

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

a = -alpha (r) (3)

solve for alpha in (3)... plug it into (2).

and you're left with

ma = -(T-mg)
T = 1/2 ma

solve for a then you can get alpha using (3)... remember the question asks for the magnitude... so once you solve it, don't worry about the minus sign if you get one.

 

[jaded18]

thanks ^^