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Hi,
Consider a spherical planet of mass m and radius rp orbiting a star with a circular orbit of radius ro (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=ωro
p=mωro
L=ro×p
|L|=|ro||p|sin(90)=|ro||p|
|L|=romωro=mωro2
Assuming that ω and ro are just magnitudes so you can leave off the absolute values.
2) I=ICM+mro2
ICM(sphere)=2mrp2/5
I=2mrp2/5 + mro2)
|L|=Iω
|L|=2mωrp2/5 + mωro2
Again, assuming ω is a magnitude.
These two answers are off by 2mωrp2/5. Where's the mistake?
Thanks in advance!
Consider a spherical planet of mass m and radius rp orbiting a star with a circular orbit of radius ro (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=ωro
p=mωro
L=ro×p
|L|=|ro||p|sin(90)=|ro||p|
|L|=romωro=mωro2
Assuming that ω and ro are just magnitudes so you can leave off the absolute values.
2) I=ICM+mro2
ICM(sphere)=2mrp2/5
I=2mrp2/5 + mro2)
|L|=Iω
|L|=2mωrp2/5 + mωro2
Again, assuming ω is a magnitude.
These two answers are off by 2mωrp2/5. Where's the mistake?
Thanks in advance!
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