1. Announcements Homework: Chapter 7 # 43, 44, 45 & 46 Solutions will be posted Monday afternoon. Exam 2 is next time. Will cover cratering, radioactive decay, gas laws fluid pressure and what is covered today: angular momentum.

2. Angular Momentum

3. Objects in orbit have orbital angular momentum For a point mass moving in a circular orbit of radius r and at a speed v, the orbital angular momentum is just L = mvr

4. Rotating objects have rotational angular momentum For solid objects we express the rotational angular momentum as the product of their moment of inertia (I) and the angular velocity they rotate at (  ). L = I  I will depend on the shape of the body and the axis of rotation.

5. Moments of Inertia The moment of inertia (I) depends on both the shape of the body and the axis of rotation. For a point mass m, moving in a circular orbit with a radius R, I = mR 2

6. If gravity is the only force acting on a system, angular momentum is conserved Internal forces cannot change the total angular momentum

7. Example The angular momentum of the Earth-Moon system consists of rotational angular momentum of both the Earth and the Moon plus the orbital angular momentum of both objects. Which part is the dominant one?

8. Example Solution Numbers that will be needed: The orbit of the Earth has a radius of 4624 km The orbit of the Moon has a radius of 384.4 km The mass of the Earth is 5.97x10 24 kg The mass of the Moon is 7.35x10 22 kg The radius of Earth is 6.378x10 6 m The radius of the Moon is 1.7375x10 6 m The orbital period of the Moon is 27.32 days Rotational period of the Earth is 86164 s

9. Example Solution 2 First find the orbital angular momentum:

10. Example Solution 3 Next find the rotational angular momentum: So, L orbit-Moon >L rot-Earth >L orbit-Earth >L rot-Moon