Rotational Dynamics: Net Torques

[henryli78]

Homework Statement

Answer: C

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

Homework Equations

∑$\tau$ = I$\alpha$
∑F = ma
a = $\alpha$r

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!

 

[tiny-tim]

hi henryli78!

∑$\tau$ = I$\alpha$
…
The torques must be balanced (is this reasoning already wrong?)

yes, the torques are balanced only if α = 0

 

[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 :)