Acceleration of a pulley/ rotational kinematics - pleaaaase help

1. Oct 18, 2007

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.
Find the magnitude alpha of the angular acceleration of the cylinder as the block descends.

_________
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 ..

2. Oct 18, 2007

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.

3. Oct 18, 2007