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abomination5
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Homework Statement
I've been working on this problem for several hours with no luck. Any help would be appreciated. (It's not homework)
A thin rod of mass M and length L is hinged at the bottom, and almost balanced vertically. It starts to fall. Find the tangential component of the force that the part of the rod below r exerts on the part of the rod above r.
(Theta is the angle between the rod and the vertical, r is the distance on the rod from the hinge)
Homework Equations
SOLN: F = Mg(L-r)(3r-L)/(4 L^2) * Sin(theta)
d x F = I *(angular acceleration)
The Attempt at a Solution
I've already determined the angular acceleration to be
3/2 g/L Sin(theta)
using the Lagrangian.
I've calculated the moment of inertia to be:
1/3 M (L-r)/L [(L-r)^2 + 3*r^2]
using the parallel axis theorem.
I've tried for several hours to get the final equation for the force but I haven't been able to do so yet... maybe there is a mistake in the moment of interia?