Calculating Net Torque for Rotational Motion with Multiple Forces

[jy1231]

Homework Statement

A solid cylinder of mass 10 kg is pivoted about a frictionless axis through the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

Homework Equations

The Attempt at a Solution

I did find the torque for each force, with the counterclockwise force being positive.

so

T(1) = (1.0 m)(5m) = 5 N*m
T(2) = (0.5 m)(6.0 N) = 3 N*m

so I figured out that the net torque would be 2 N*m in the clockwise direction.

But i don't know what to do with this.

Thank you so much!

 

[SammyS]

The problem as stated doesn't indicate in which direction (clockwise or counter-clockwise) either force will tend to make the cylinder rotate.