Yo-Yo Motion Puzzle - Find the Speed & Time of Fall

[lfabb]

Homework Statement

The string in a yo-yo is wound around an axle of radius 0.512 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.206 kg and outer radius 1.88 cm. Starting from rest, it rotates and falls a distance of 1.20 m (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle. What is the speed of the yo-yo when it reaches the distance of 1.20 m? How long does it take to fall?

Homework Equations

mgh=1/2mv^2+1/2Iw^2
I=1/2mr^2
w=v/r

The Attempt at a Solution

r1=.512
r2=1.88
mgh=1/2mv^2+1/2(1/2mr2^2)(v/r2)^2

The answer is obviously incorrect. What exactly am I doing wrong? Thanks!

 

[Redbelly98]

You're almost there, there's just a small change to make in your equation.

w depends on the radius at which the string is located.

The string isn't wound around the outside of the yo-yo (r2 that you used in w=v/r), so think about where the string is wound on the yo-yo.

p.s. welcome to PF.