# Physical pendulum problem

1. Dec 4, 2013

### dzidziaud

1. The problem statement, all variables and given/known data
Two identical thin rods, each with mass m and length L, are joined at right angles to form an L shaped object. This object is balanced on top of a sharp edge. If the L shaped object is deflected slightly, it oscillates. Find the frequency of oscillation.
Here is a picture:
http://www.luiseduardo.com.br/undulating/SHM/shmproblems_arquivos/image111.jpg [Broken]

2. Relevant equations
moment of inertia of a slender rod about one end: I = 1/3mL^2
ω=√(mgd/I)

3. The attempt at a solution
I think the center of mass is at 45° between the rods, √2/2L down from the pivot. Let me know if that is wrong. I think that would make d=√2/2L. So my main problem is in finding I. I know I for each rod, but I don't know how to use that to find I for the entire oscillating object.

Last edited by a moderator: May 6, 2017
2. Dec 4, 2013

### voko

Moment of inertia is additive. If you know the moments of inertia of two bodies (with respect to one point), then the moment of inertia of the combined body (with respect to the same point) is the sum of the moments.

3. Dec 4, 2013

### dzidziaud

What do I do to take the angle into account?

4. Dec 4, 2013

### voko

Why would you? Are there any angles in the definition of the moment of inertia?

5. Dec 4, 2013

### dzidziaud

Well, no. But the answer I am getting is just a factor of pi/2 off from the correct answer, but I don't know where that is coming from.

6. Dec 4, 2013

### voko

What frequency are you supposed to find? Angular $\omega$ or ordinary $f$?

7. Dec 4, 2013

### dzidziaud

Oh my goodness, you're right. I've been looking for the angular frequency when this question calls for regular frequency. Thank you so much! I can't believe I wasted so much time on such a silly oversight :P