# Rotation: disk and pulley

1. Nov 23, 2013

### Avi Nandi

1. The problem statement, all variables and given/known data

A disk of mass M and radius R unwinds from a tape wrapped around it. The tape passes over a frictionless pulley and mass m is suspended from the other end. Assume that the disk drops vertically.

a. relate the accelerations of mass m and disk ,a and A, respectively to the angular acceleration of the disk.

b. Find a, A and α.

2. Relevant equations

3. The attempt at a solution

equations of motion : T - mg = ma
T - Mg = MA

-TR = $\frac{1}{2}$MR$^{2}$α

Are these equations of motion wrong????

2. Nov 23, 2013

### haruspex

Which direction are you taking as positive, up or down? If up, I would write that as ma = T + mg etc., where g takes a negative value. But it's maybe a matter of personal preference.
They look ok to me, but you've not written out the relationships between A, a, α and R. That is where this question fools some people.

3. Nov 24, 2013

### Avi Nandi

I took up as the positive direction. But I think T and g are always opposing each other. I have written a constraint equation A + a = Rα. But the clue given in the book is " if A= 2a then α= 3A/R"

4. Nov 24, 2013

### Saitama

That's a typo in the book. There was a thread on the same problem recently.

5. Nov 24, 2013

### haruspex

The consensus is that it's an error in the book. It should say α= 3a/R. See https://www.physicsforums.com/showthread.php?t=722327