Angular Velocity from Potential and Mechanical Energy of rotating rod

[jstep]

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
K_f + U_f = K_i + U_i

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!

 

[eczeno]

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

 

[jstep]

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

 

[eczeno]

correct.

 

[jstep]

thanks so much!