Torque, τ:

$\overline{){\mathit{\tau}}{\mathbf{=}}{\mathit{\alpha}}{\mathit{I}}}$

or

$\overline{){\mathit{\tau}}{\mathbf{=}}{\mathit{r}}{\mathit{F}}}$

The tensions are in the opposite direction.

ΣF = T_{2} - T_{1} = 12 - 10 = 2N

τ = (0.31)(2) = 0.62 N•m

A frictionless pulley, which can be modeled as a 0.90 kg solid cylinder with a 0.31 m radius, has a rope going over it, as shown in the figure. The tensions in the rope are 12N and 10N. What is the angular acceleration of the pulley?