How Long to Increase Spool's Angular Velocity from 11.0 to 35.0 rad/s?

[dana711]

Homework Statement

A spool of thin wire rotates without friction about its axis. A man pulls down on the wire with force of 14.9N. How long does it take to increase the angular velocity of the spool from 11.0rad/s to 35.0rad/s?
Icm = 0.490kg*m^2
Inner radius, r = 0.280m
Outer radius, R = 0.600m

Homework Equations

w=d(theta)/dt
w=v/r

The Attempt at a Solution

im not sure how to do this. i know the equation for angular velocity but i don't know what to do with the force and time

 

[Doc Al]

Figure out the angular acceleration using Newton's 2nd law for rotation.