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A rod of mass M and length L is connected to a pivot at one of its ends. The pivot is hanging from a horizontal ceiling and the rod is set parallel to the ceiling (its also horizontal). The force that will cause it to rotate once it is released is gravity and what I need to find is the initial angular acceleration of the rod and the initial linear acceleration of its right end.

For T (torque) and @ (angular acceleration), if we were to mathematically use T = Fd for d = rsin(X), and Net T = I@, the @ found would be the same at any point on the rod, so it would be acceptable to use L as the length, L/2 as the length, and so forth to find @ while the force acting on the rod, gravity, is perpendicular to it. Therefore F = Mg and T = Mgrsin(X), in which sin(X) equal to 1. Therefore T = Mgr. Using that and T = I@, then @ = T/I = Mgr/(1/3*M*L^2). Now all that is needed is to plug in for r, which could supposedly be the length for any point along the rod. But if I were to plug in random values of r, for 0 < r

For T (torque) and @ (angular acceleration), if we were to mathematically use T = Fd for d = rsin(X), and Net T = I@, the @ found would be the same at any point on the rod, so it would be acceptable to use L as the length, L/2 as the length, and so forth to find @ while the force acting on the rod, gravity, is perpendicular to it. Therefore F = Mg and T = Mgrsin(X), in which sin(X) equal to 1. Therefore T = Mgr. Using that and T = I@, then @ = T/I = Mgr/(1/3*M*L^2). Now all that is needed is to plug in for r, which could supposedly be the length for any point along the rod. But if I were to plug in random values of r, for 0 < r

__<__L, then I would get a different @ for different lengths. Is it customary to use the center of mass for r?
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