# Rotational Dynamics: Net Torques

1. Jan 2, 2014

### henryli78

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

Note: Sorry admins for the picture, needed to include the diagram though.

2. Relevant equations
∑$\tau$ = I$\alpha$
∑F = ma
a = $\alpha$r

3. The attempt at a solution
The torques must be balanced (is this reasoning already wrong?), thus,
F*R1 = F_T*R2
F_T = FR1/R2
The only force acting on the block is the F_T, thus the acceleration is FR1/mR2

Why are the torques not balanced in this case? If not, how do I exactly relate the moment of inertia of the entire disk to fit into the entire problem? Thank you in advance for the help!

Last edited: Jan 2, 2014
2. Jan 2, 2014

### tiny-tim

hi henryli78!
yes, the torques are balanced only if α = 0

3. Jan 2, 2014

### henryli78

Thank you! I solved it.

I wrote out:
Net Torque = I*alpha = I*a/R2 = F*R1 - T*R2
T = ma, thus I*a/R2 = F*R1 - m*a*R2
I*a/R2 + m*a*R2 = F*R1
a(I/R2+mR2) = F*R1
a(I + mR2^2) = F*R1*R2
a = F*R1*R2/(I+mR2^2)

Thank you very much for the help :)