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Would a rod, hinged at one end to a wall, have a constant angular acceleration if released at 45 degrees?
So i'm doing a problem for my dynamics class, and there is a rod that is hinged on one end to a wall. It is released from rest at 45 degrees from the horizontal.
What I want to know, is will the angular acceleration remeain constant since it is influenced only by gravity, or will it vary, since the magnitude of the moment is dependent on the of the rod?
I am just trying to find out if I will be stuck with a second order differential equation, or if the angular acceleration from 45 degrees to the horizontal is dependent only on that initial angle.
*on the ANGLE of the rod (for that second section)
Crud. So I take it there's no easy way to find the velocity of the endpoint when the angle is zero degrees then?
1 Answer
- markumLv 51 decade agoFavorite Answer
Bad news - although the moment of inertia is a constant and unaffected by any angles, the problem is that the torque changes as the angle changes.
Net torque = I * alpha
R x F = I * alpha
but R x F = (length / 2) * W * cos(angle)
where angle is the angle of the rod versus the vertical direction, and W is the weight. Since the angle is constantly changing, the angular acceleration alpha will also be constantly changing.
Often a small angle approximation is used for pendulums, but 45 degrees is not a small angle.