Mastering Physics: Acceleration of a Pulley

1. Apr 15, 2017

danielhep

1. The problem statement, all variables and given/known data
A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1) . 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 α of the angular acceleration of the cylinder as the block descends.

2. Relevant equations
F=ma=mg-T
Torque=Iα=-Tr
a=-rα
I=mr2/2
3. The attempt at a solution
I use these three equations to eliminate T and solve for α.

m(-rα)=mg-T
-1/2mr=T
-mrα=mg+1/2mr
-α=g/r+1/2
α=-1/2-g/r

I tried this answer however it was wrong.

Mastering says the correct answer is
α = 2g/3r

I'm really not sure where this comes from, so any help would be great! I need to understand where I went wrong.

2. Apr 15, 2017

TomHart

Where did this come from? It doesn't look right.

Edit: Okay, now I see what you did. You were equating Iα to -Tr, then substituting I = mr2/2 for I. You should work through that algebra again and I think you'll find your problem.

3. Apr 15, 2017

danielhep

I dropped the g. Thank you so much! I found the correct answer.