Fr = m alpha (L/2) cos(beta)

N - mg = - m alpha (L/2) sin(beta)

Fr cos(beta) - N sin(beta) = 2 Io alpha / L

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The problem is a dynamics problem for an engineering class im in and i've gotten the three equations (which is suppose to be the hard part) that I have to simoltaneously solve. Knowns in the above equation include 'm', 'g', and beta and everything must be in terms of these variables.

Also Io = (mL^2)/12

I'm trying to solve for Fr and N in terms of known quantities but i keep getting stuck with some messy algebra and wrong answers. Any help would be greatly appreciated.