Falling yo-yo attached to string

[Jeptha]

1.Homework Statement

A giant yo-yo of mass 410 kg measuring about
1.2 m in radius was dropped from a platform
63 m high. One end of the string was tied
to the platform, so the yo-yo unwinds as it
descended. Assuming that the axle of the yo-yo has a
radius of 0.3 m, find the velocity of descent at
the end of the fall. The acceleration of gravity
is 9.81 m/s
Answer in units of m/s.

Homework Equations

M=410 kg
R=1.2 m
h=63 m
r=0.3 m
g=9.81 m/s²

mgh = 0.5Iw² +0.5mv²

I = 0.5MR²

w = v/R

The Attempt at a Solution

So I've been trying to figure this problem out since last night. Please be patient with me. I've always struggled with problems involving rotational motion for some reason. If I'm understanding this right, the potential energy will be split up into the translational kinetic energy and the rotational kinetic energy. My problem is that I'm having a REALLY hard time visualizing how to break up the rotational energy. I'm assuming that my equation for I (the moment of inertia) is where my problem is because there's torque from gravity and tension from the string, but I don't really understand how I'm supposed to incorporate that.

In my first attempt at a solution, I substituted I and w into my equation for mgh, and after doing some algebra, I came up with v = 2*sqrt(gh/3) and that obviously gave me a wrong answer.

Can someone explain to me what I'm doing wrong conceptually?

 

[member 553083]

I really don't understand why my equation for I isn't working. And how should I properly break up the rotational energy in this problem? Thanks