# Angular Velocity from Potential and Mechanical Energy of rotating rod

## Homework Statement

I am asked to find the angular velocity of a falling rod in the instant that the rod meets the horizontal. The system is set up in this image:

The only force acting on the rod is gravity

## Homework Equations

U = (1/2)MgL
K = (1/2)Iw2
Kf + Uf = Ki + Ui

## The Attempt at a Solution

Can I solve this by using the potential energy of the rod with this equation:

U = (1/2)MgL

and then equating that to the Mechanical Energy at the point that it meets the horizontal?

I know the moment of inertia of the rod so if I do (1/2)MgL = (1/2)Iw2 and solve for omega, is that correct?

Also, when finding the initial potential energy, should i use the full length of the rod or only the length to the center of mass?

Thank you!

Related Introductory Physics Homework Help News on Phys.org
yes, you are correct. to calculate the initial potential energy, just use the altitude of the center of mass and drop the (1/2), that should not be there.

good luck

Oh okay, so let me just make sure I understand:

so this is the correct way to find the initial potential energy?

U = mgLsin$$\theta$$

where L is the length to the center of mass

correct.

thanks so much!