- #1

Redwaves

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- Homework Statement
- Consider a planet orbiting the fixed sun. Take the plane of the planet's orbit to be the xy plane, with the sun at the origin and label the planet's position by polar coordinates (##r,\phi##). Show that the planet's angular momentum has magnitude ##L = mr^2\omega##, where ##\dot\phi## = ##\omega##

- Relevant Equations
- ##\vec{L} = \vec{P} \times \vec{r}##

##\vec{L} = \vec{P} \times\vec{r}##

##L = mvr sin \phi##, where P = mv

Since ##\vec{r}## and ##\vec{v}## are always perpendicular, ##\phi## = 90.

Then, ##L = mvr##

At this point, I don't see how to get ##L = mvr = mr^2\omega##, using ##\omega = \dot{\phi}##

I know that ##\omega = \frac{v}{r}##. However, the way the question if written, I'm wondering if there's another by way using the angle ##\phi##.

##L = mvr sin \phi##, where P = mv

Since ##\vec{r}## and ##\vec{v}## are always perpendicular, ##\phi## = 90.

Then, ##L = mvr##

At this point, I don't see how to get ##L = mvr = mr^2\omega##, using ##\omega = \dot{\phi}##

I know that ##\omega = \frac{v}{r}##. However, the way the question if written, I'm wondering if there's another by way using the angle ##\phi##.

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