Finding Angular Velocity of a Yo-Yo with a Pulled String

[Physics122]

Homework Statement

Realize I'm asking a lot of question today, but I'm working on a huge physics project and I'm not asking for answers, just some guidance where I'm stuck

A certain yo-yo can be modeled as a uniform cylindrical disk with mass M and radius R and a lightweight hub of radius ½R. A light string is wrapped around the hub.

imagine that that you pull upward on the string such that the yo-yo remains in the same place. Find the angular velocity of the yo-yo when you have pulled the string upward a distance of L.

Homework Equations

Torque = r x F
Work = change in kinetic energy
torque = I x angular acceleration
only rotation = change in (1/2 I w^2)

The Attempt at a Solution

w²=w₀² +2(alpha=angular acceleration) * (theta -theta₀) -->

torque = I (W²/2(theta-theta₀) -->

torque * change in theta = 1/2*I*w²

Now I just need to figure out how to find theta or what to do with it? Maybe get it in terms of L? but how? Does torque * change in theta = the change in kinetic energy?

 

[vela]

Hint: You also need F=ma.