## 18. Classical Mechanics (Angular Momentum)

##### Solution

Angular momentum in circular motion is

where is angular momentum, is the mass of the satellite, is the velocity, and is the orbital radius. In this problem, two satellites are identical. So the mass of the satellite is equal. The orbital radius of A is the ratio of the angular momentum of A to the twice that of B, so

Since satellites have circular motion, the centripetal force is equal to the gravitational force

where is the mass of the Earth. The orbital velocity of the satellite can be obtained as

Then we can wirte angular momentum as

Therefore, the ratio of the angular momentum is

##### Answer

(C)

##### Reference

https://en.wikipedia.org/wiki/Angular_momentum#Scalar_—_angular_momentum_in_two_dimensions