# Homework Help: Rod Pendulum (high school circular motion)

1. Feb 18, 2010

### jumbogala

1. The problem statement, all variables and given/known data
A rod of mass m and length L is suspended from one end, and swings as a pendulum (ignore friction from the hinge). It is released from rest when it forms an angle θ with respect to the vertical.

The moment of inertia of the rod about its rotation axis is mL2/3.

What is the speed of the center of mass of the rod?
What is the angular speed of the rod?
What is the speed of the free end of the rod?

2. Relevant equations

3. The attempt at a solution
I don't even know where to start this question.

I want to use conservation of mechanical energy:
(1/2)Iω20 + mgh0 = (1/2)Iω2f + mghf

Then ω0 is zero so it starts from rest. Also, make the 0 height mark where the center of mass hits at the horizontal. So that leaves me with:

mgh0 = (1/2)Iω2f

But, how do I find the initial height!? and once I do that I need to somehow get speed out of ω.

Last edited: Feb 18, 2010
2. Feb 18, 2010

### jumbogala

So I did figure some of it out. Using trig I found the height to be Lsin2(θ/2)

And solving that equation I gave before gives sqrt(6g/L)*sin(θ/2) = ωf

Now what I'm confused about is if I can just multiply that ω by L/2 to get the speed at the center of the rod and L to get it at the end of the rod.