(a) What is the angular momentum of the Moon in its orbit around Earth? (b) How does this angular momentum compare with the angular momentum of the Moon on its axis? Remember that the Moon keeps one side toward Earth at all times. (c) Discuss whether the values found in parts (a) and (b) seem consistent with the fact that tidal effects with Earth have caused the Moon to rotate with one side always facing Earth.
Step-by-step solution Step 1 of 6 The orbital angular momentum of the moon of mass in its orbit around the Earth of radius is calculated as, Here, is the moment of inertia of the Moon in its orbit around the earth and is the angular speed of the moon revolving around the Earth. Recall that the moment of inertia of the moon revolving around the earth is, Replace with in . Step 2 of 6 (a) The Moon takes time (T ) of 27.3 days to complete its revolution. So, the angular velocity is calculated as, Substitute 27.3 days for T . Su bstitute for M, for r and for in formula for angular momentum . Hence, the angular momentum of moon is . Step 3 of 6 (b) The moon takes almost 27.3 days to rotate on its own axis, since the rotational period is exactly the same as the orbital period, so the same portion of the moon is always facing the earth. So, the angular velocity for rotation of moon about its own axis is equal to revolution of moon around Earth. Now the angular momentum of the moon rotating on its own axis is calculated as, Here, is the moment of inertia of the Moon revolving around the Earth and is the angular velocity of the Moon rotating on its own axis. The moment of inertia of the moon is calculated as, Here, is the radius of the Moon. Substitute for in formula for angular momentum. Substitute for , for and formula for angular momentum. The angular momentum of moon around its axis is