## Question

The moon’s mass is 7.4×1022kg and it orbits 3.8×108m from the earth with a period of 27.3 days. part a what is the angular momentum of the moon around the earth?

## Answer

The angular momentum of the Moon around the Earth is given by:

where m is the Moon’s mass, v its speed and r the radius of the orbit.

We already have the mass, m and the radius of the orbit r, so we need to find the velocity first. Assuming the orbit of the Moon is like a circle, the velocity is the perimeter divided by the time to complete one orbit:

The time t is (keeping in mind that 1 day=86400 s):

So the velocity is:

And so we can finally calculate the angular momentum of the Moon around the Earth: