Spinning rod dropping on a pivot

AI Thread Summary
The discussion revolves around a physics problem involving a long, thin rod pivoting at its base after being pushed. Participants suggest using conservation of energy to analyze the system, focusing on the transition of potential energy to kinetic energy as the rod falls. The key equations involve the moment of inertia and angular velocity, with an emphasis on rotational kinetic energy. The center of mass's potential energy is considered crucial in determining the rod's motion. The conversation highlights the need to account for both rotational and translational motion as the rod impacts the table.
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Homework Statement


a long, thin rod of mass M and length L is standing stright up on a table. its lower end rotates on a frictionless pivot. a very slight push causes the rod to fall over. as it hits the table, what are (a) the angular velocity and (b) the speed of the tip of the rod?


Homework Equations





The Attempt at a Solution


could we set up a conservation of energy equation for this?
1/2I(for spinning of rod)\omega^2 + mgh = 1/2 I(for spinning of rod)\omega^2 + 1/2I(for dropping of rod)\omega^2
 
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I'd suggest that there is only rotational kinetic energy to consider.

And it gets fed by the PE of the center of mass doesn't it?
 

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