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

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To find the angular velocity of a yo-yo when the string is pulled upward a distance L, the relationship between torque, angular acceleration, and kinetic energy must be utilized. The equations provided, including torque = r x F and work = change in kinetic energy, are essential for solving the problem. The challenge lies in expressing the angular displacement (theta) in terms of the distance L pulled. It is suggested to relate torque and angular displacement to the change in kinetic energy, while also considering the force applied (F=ma). Understanding these relationships will lead to the correct calculation of angular velocity.
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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?
 
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Hint: You also need F=ma.
 

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