- #1

Isaac0427

Gold Member

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Hi,

Consider a spherical planet of mass m and radius r

1) p=mv

v=ωr

p=mωr

L=r

|L|=|r

|L|=r

Assuming that ω and r

2) I=I

I

I=2mr

|L|=Iω

|L|=2mωr

Again, assuming ω is a magnitude.

These two answers are off by 2mωr

Thanks in advance!

Consider a spherical planet of mass m and radius r

_{p}orbiting a star with a circular orbit of radius r_{o}(distance from axis of orbit to the planet's center of mass). The planet has an angular velocity ω. Say we wanted to find the magnitude of the angular momentum of the planet. Going about that two different ways provides two different answers--which one is correct?1) p=mv

v=ωr

_{o}p=mωr

_{o}L=r

_{o}×p|L|=|r

_{o}||p|sin(90)=|r_{o}||p||L|=r

_{o}mωr_{o}=mωr_{o}^{2}Assuming that ω and r

_{o}are just magnitudes so you can leave off the absolute values.2) I=I

_{CM}+mr_{o}^{2}I

_{CM(sphere)}=2mr_{p}^{2}/5I=2mr

_{p}^{2}/5 + mr_{o}^{2})|L|=Iω

|L|=2mωr

_{p}^{2}/5 + mωr_{o}^{2}Again, assuming ω is a magnitude.

These two answers are off by 2mωr

_{p}^{2}/5. Where's the mistake?Thanks in advance!

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