Calculating Angular Speed of Rotating Apparatus with Attached Mass and Rod

[JiggaMan]

Homework Statement

The 3.0 kg rod has a length of 80 cm. The 4.0 kg rectangle attached to the rod has negligible dimensions. The entire object rotates counterclockwise about the bottom of the rod. Determine the angular speed of the apparatus at the instant the rod is horizontal.

https://gyazo.com/9d0bb4ce2fed98b192f173a918549f60

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Homework Equations

mgh = potential energy
( w^2 * i ) * .5 = rotational energy
i = moment of inertia
moment of intertia for rod rotated on end = (m * L^2) * .333
L = length
m = mass
w = angular speed
THE ANSWER SHOULD BE 5.19 rad/s

The Attempt at a Solution

*For the height, I found the center of gravity which is .63 meters, i think the length stays .8 though
mgh = (w^2 * i ) * .5
mgh = (w^2) * (m * L^2) * .333 * .5
7 * 10 * .63 = ( w^2 ) * (7 * .8 * .8 ) * .333 * .5
44.1 = (w^2) * .746
59.115 = (w^2)
7.68 = w
7.68 rad/s ?[/B]

 

[JiggaMan]

Being the genius I am, I have self-analyzed my own work and found my error. For the rotational energy. I must find the rotational energy of the mass first, then the rod:
( ( w^2 ) * .5 * 4 * .8 * .8 ) and ( ( w^2 ) (3* .8 * .8 ) / 3 ) then add them and take out the w ^ 2 since the angular acceleration should be equal for both:
( w^2 ) ( (.5 * 4 * .8 * .8 ) + ( ( 3 * .8 * .8 ) /3 ) )
I was however correct to have found the center of gravity for mgh.