Final answer:
The angular momentum of the Moon in its orbit around Earth can be calculated using the formula: L = I * ω, where I is the moment of inertia and ω is the angular velocity. By substituting the given values and solving the equation, we can determine the angular momentum of the Moon.
Step-by-step explanation:
The angular momentum of an object in orbit is equal to the product of its moment of inertia and angular velocity.
The moment of inertia of a spherical object can be calculated using the formula:
I = (2/5) * m * r^2
where m is the mass of the object and r is its radius.
In this case, the mass of the Moon is 7.35×10²² kg and its radius is 1.74×10⁶ m. Using these values, we can calculate the moment of inertia of the Moon:
I = (2/5) * (7.35×10²²) * (1.74×10⁶)^2
Once we have the moment of inertia, we can calculate the angular momentum using the formula:
L = I * ω
where ω is the angular velocity of the Moon. Since the Moon completes a full rotation every 27.3 days, we can convert this to radians per second:
ω = (2π) / (27.3 * 24 * 60 * 60)
Substituting the values into the equation, we find:
L = (2/5) * (7.35×10²²) * (1.74×10⁶)^2 * (2π) / (27.3 * 24 * 60 * 60)
Now we can calculate the angular momentum of the Moon in its orbit around the Earth.