# Finding angular velocity using conservation of angular momentum

1. Jul 26, 2009

### cosurfr

Hello everyone, I hope that someone can help me solve this rather than solving it for me, heres the problem and what i've done so far....oh and thanks in advance!

1. The problem statement, all variables and given/known data

A thin rod has a length of 0.25 m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.32 rad/s and a moment of inertia of (1.1 x 10^-3 kg x m^2). A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (mass = 4.2 x 10^-3kg) gets where it’s going, what is the angular velocity of the rod?

2. Relevant equations
*Lf=angular momentum final
*Lo=angular momentum initial

Conservation of angular momentum: L=Iw -> Lf=Lo -> Iwf=Iwo, wo=0
Iwf=0

3. The attempt at a solution
Okay so I thought this problem seemed fairly straight forward, so hopefully i'm just doing a little algebra incorrectly or something, but heres my whirl at the answer
Iwf=0
(Moment of Inertia of rod)(ang vel of rod)+(mass of bug)(length of rod)^2(w)=0

(1.1 x 10^-3 kg x m^2)(0.32 rad/s) + (4.2 x 10^-3kg)(0.25m)^2(w)=0

(4.2 x 10^-3kg)(0.25m)^2(w)= -(1.1 x 10^-3 kg x m^2)(0.32 rad/s)

*****Now just solve for w? Or is this completely wrong? I did do the calculations but didnt want to put all that up if this wasnt even the right way to set up the problem. If someone could let me know if i'm on the right track and lend me a hint of how to proceed i'd really appreciate it. Thanks

Cosurfr
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 26, 2009

### JazzFusion

Why did you use w0 = 0?

Go back towards the top of your proof, and use this given value for w0 instead ... see what happens.

3. Jul 26, 2009

### cosurfr

Thanks so much. Thats exactly where i went wrong. The initial ang vel of the bug would have been the same as the initial ang vel of the rod (constant). That cleared it all up. Thanks a ton for not just doing it for me but rather helping me find the way. This website is the best FYI

cosurfr