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## Homework Statement

A planck of length L2 leans against a wall. It starts to slip downwards without friction. Show that the top of the plank loses contact with the wall at 2/3 of it's original height.

## Homework Equations

F*R = torque

Moment of Inertia of Rod (I) = 1/3 M4L[tex]^{2}[/tex]

Mgh = [tex]\frac{1}{2}[/tex]MV[tex]^{2}[/tex] + [tex]\frac{1}{2}[/tex]I[tex]\omega[/tex][tex]^{2}[/tex]

## The Attempt at a Solution

I've been trying this problem for over two hours now and can't seem to get it to work. My initial idea was to work with torques, but I didn't seem to be getting anywhere so I tried the Mgh formula above, setting h as the height of the center of mass (1/2h) and trying to solve for h knowing that at the point the rod leaves the wall the horizontal velocity should be equal to the horizontal component of the radial velocity. So far I can't seem to get the equations to work out, any help would be very much appreciated.

The problem also has a hint:

Only a single variable is needed to describe the system. Note the motion of the center of mass.