What is the angular momentum of the Moon in its orbit around Earth?
I assume I need the mass of the moon, radius of the moon, and angular velocity of the moon. Found those on google, plugged them into my formula (angular momentum = Iw) and got the wrong answer...
I used moment of inertia = (2mr^2)/5
mass = 7.34767309 × 10^22 kg
radius = 1,737,000 meters
angular velocity = 2.43 x 10^-7
Which of these values is wrong?
Moment of Inertia for a mass rotating about a point: mr^2
angular momentum=mr^2w=mr^2*2PI/period)
look period up, about 27.3 days, convert to seconds
The orbital angular momentum of the Moon is about 2.9 x 10^34 kgm^2/s
To calculate the angular momentum of the Moon in its orbit around Earth, you need the correct moment of inertia. The formula you used for moment of inertia, I = (2mr^2)/5, is incorrect for a sphere like the Moon. The correct formula for the moment of inertia of a solid sphere is I = (2/5)mr^2.
By plugging the correct values into the formula, you can calculate the angular momentum. Let's do the calculation:
Mass of the Moon (m) = 7.34767309 × 10^22 kg
Radius of the Moon (r) = 1,737,000 meters
Angular velocity of the Moon (w) = 2.43 x 10^-7 rad/s
Moment of inertia (I) = (2/5) * (mass) * (radius)^2
= (2/5) * (7.34767309 × 10^22 kg) * (1,737,000 meters)^2
Now, you can substitute the correct values into the equation and calculate the moment of inertia. Then multiply the moment of inertia by the angular velocity to find the angular momentum.
If you solve all the calculations correctly, you will get the correct value for the angular momentum of the Moon in its orbit around Earth.