# Am I doing this conservation of angular momentum problem correctly? [closed]

I am doing some calculations for a practical project of mine. Basically I have a levitating sphere with gravity countered and close to 0 friction when the sphere rotates(due to airdrag). Inside the sphere is a servo spinning at $.12sec/60 degrees$, or $2\pi /.72sec$(8.73 rad/s). The spinning servo on the inside has masses attached to both arms to allow it to have enough moment to make the globe spin. The arm's radius is 1 or .0254m.

I have the following equation:

JA=sum of torques on globe due to servo


J is the moment of inertia for the sphere and many other things inside, I did a rough calculation and got .5kg·m²

A is the angular acceleration, for now i have it be $\pi /6$ radians, I assume that this acceleration is good enough for the globe to turn at a reasonable rate.

Finally to find the torques, there are two torque motion on the servo, since its servo arm has two arms. All I need to do is calculate the torque on one arm and multiply by 2. $\omega$ is the angular velocity of the servo, r is the radius of the arm. m is the mass attached to the end of the servo arm, and v is the velocity. Assume the servo arm itself is massless.

$F=ma$

$T=Fr$

$a=\omega v$

$velocity=\omega r$

$F=m\omega \omega r$

$T=m\omega \omega rr$

Now to solve:

$T=m\omega ^2r^2$

$2T=m\omega ^2r^2$

$2T=JA$

$m\omega ^2r^2=JA$

$m=JA/(\omega ^2r^2)=.5(\pi /6)/(8.73^2*.0254^2)=5.324grams$

Thus, to make my globe rotate(at $\pi /6$ angular acceleration) in reaction to the servo on the inside spinning, the servo must hold $5.3 grams$ of weight on both ends.

Does this calculation make sense?

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Is there a reason you think it doesn't make sense? It'll help us give a more focused answer if you explain why you're wondering about your result. – David Zaslavsky Sep 24 '11 at 4:19
@DavidZaslavsky its not that I don't think it doesn't make any sense. But I'm unsure if I'm taking the right steps and setting up the right equations. I just needed some help to verify my approach – mugetsu Sep 24 '11 at 8:31
OK, well then, how else do you think you should be doing it? I mean, clearly there's something you're not sure of, otherwise you wouldn't be asking the question. I'm trying to get you to ask about the specific concept you're unsure about, since it'll make a much more useful question. This site is really meant for questions about physical concepts, not general "check my math" questions. – David Zaslavsky Sep 24 '11 at 19:25
@DavidZaslavsky I'm not sure if my concept of sum of torque from the arms=moment of inertia of body * angular acceleration of body is applicable here. As you can see I did a lot of substitution, playing around with omega. The specific concept I'm not understanding would have to be how conservation of angular momentum would work in a system that essentially applies torque to itself. – mugetsu Sep 27 '11 at 0:33

## closed as too localized by David Zaslavsky♦Dec 20 '12 at 1:26

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