The figure below shows a rigid assembly of a thin hoop (of mass m and radius R =

Question

The figure below shows a rigid assembly of a thin hoop (of mass m and radius R = 0.160 m) and a thin radial rod (of mass m and length L = 3.00 R). The assembly is upright, but if we give it a slight nudge, it will rotate around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in such a nudge is negligible, what would be the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?

Really Confused on how to find I and solve for Radians.

Explanation / Answer

The total moment of inertia of the loop is
        I = [(mL2 /12 + mL2 / 4] + 0.5mR2 + m(L+R)2
         = mL2 / 3 + 1/2mR2 + m(L+R)2       From law of conservation      1/2 I2 = m g L + 2 m g (L+R)      =    [ 2* (m g L + 2 m g(L+R)) /   I ]    substituting the values L = 3.00 R , R = 0.160m , mass is m to get solution

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