|Feb14-12, 10:50 PM||#1|
Angular Velocity and Spin/Orbital Angular Momentum of Jupiter
Calculate spin angular momentum of Jupiter
L = Iω
I = (2/5)*M*r2 (for a uniform sphere)
ω = (G*M/r3)1/2 (I calculated this earlier in the homework, but I've looked it up and I think it's right)
Attempt at a Solution:
I thought this should be pretty straight forward, but when I calculated Jupiter's rotational angular momentum, it was slightly off. I've narrowed it down to my angular velocity equation being incorrect; when I used the published value for Jupiter's angular velocity, I got the right angular momentum.
I then went back and checked the value for ω (.0005887 1/s) which correlated to a rotational period of around 3 hours, and that clearly isn't right. Does anyone have any idea where I'm going wrong here?
I got the equation for ω when I calculated the minimum rotation period of a star by equating the gravitational force and the centrifugal force. The homework asks if the period of a star (T=2∏/ω) differs from that of a planet, but I don't see why it should. I was thinking perhaps there was a difference I was missing and that's why my calculations weren't coming out as expected, but my ω for the sun is off too (I just didn't have the exact numbers to give you guys).
|Feb15-12, 11:57 AM||#2|
Your question asks for the "spin" angular momentum. Be careful not to confuse that with the orbital angular momentum.
|Feb15-12, 12:31 PM||#3|
You calculated the angular velocity of Jupiter around the Sun instead of the angular velocity of Jupiter's spin.
None the less, your number for Jupiter's angular velocity is still wrong. Jupiter takes 9 hours 55 minutes and 30 seconds to rotate 360 degrees, or 2 pi radians. Divide 2 pi by your sidereal day to get the angular velocity of Jupiter's spin.
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