Calculating Alpha: Magnitude of Angular Acceleration??

[merlos]

calculating alpha??

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.
Express your answer in terms of the cylinder's radius r and the magnitude of the acceleration due to gravity g.




Acceleration of the block is = g
Force acting on the block is = mg
The torque by this force on the cylinder about the axis = mgr
This results in accelerating the rotation of the cylinder.
mgr = I x alpha, where I = moment of inertia of the solid cylinder;
alpha = Angular acceleration of the cylinder.

I = (1/2)mr^2

alpha = torque/I = mgr/I = 2g/r
??

 

[Doc Al]

Acceleration of the block is = g
Force acting on the block is = mg

That would be true if the block was in free fall. But I assume it's tied to the string that's wrapped around the cylinder.