(17%) Problem 5: The Moon orbits around the Earth and also spins on its axis. 33% Part (a) What is the angular momentum of the Moon in its orbit around Earth?

33% Part (b) What is the angular momentum of the Moon in its rotation around its axis? A 33% Part (c) How many times larger is the orbital angular momentum than the rotational angular momentum for the Moon?

## Answer

The angular velocity of the moon is as follows: 21 21 (1 day 1 hr 1 min I 27.3 days 24 hr 60 min 60 s = 2.66×10- rad’s O = a The angular momentum of the moon in this case is, L = 10 = mR?o=(7.35x10kg (3.84×108 m) (2.66×10- rad’s) = 2.89×104 kg-mºls b) Since the moon is always facing the earth, the angular velocity of the moon about its own axis is same as the angular velocity of the moon around the earth. The angular momentum of the moon in this case is as follows: 2 1 =10 =< mr?o=(7.35×10^2 kg)(1.74×109 m)? (2.66×10“ rad’s) = 2.37×10 kg-m /s c) The ratio of the angular momentum for revolution to the rotation can be calculated as follows: 2.89 x1034 kg-m/s – 122×105 2.37×1029 kg-m/s Thus, the angular momentum of moon revolving in orbit is 1.22×10 times larger than the rotational angular momentum.