announcements homework: chapter 7 # 43, 44, 45 & 46 solutions will be posted monday afternoon....

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.

Angular Momentum

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

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 (w).

L = Iw

I will depend on the shape of the body and the axis of rotation.

Moments of InertiaThe 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 = mR2

If gravity is the only force acting on a system, angular

momentum is conserved

Internal forces cannot change the total angular momentum

ExampleThe 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?

Example SolutionNumbers 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 5.97x1024 kg• The mass of the Moon is 7.35x1022 kg• The radius of Earth is 6.378x106 m• The radius of the Moon is 1.7375x106 m• The orbital period of the Moon is 27.32 days• Rotational period of the Earth is 86164 s

8

sec

6

sec

2

2 3.844 101023

27.32 86400

2 4.624 1012.31

27.32 86400

msMoon

day

msEarth

day

circumference rv

period T

mv

days

mv

days

Example Solution 2First find the orbital angular momentum:

2

2

24 6 32

22 8 34

5.97 10 12.31 4.624 10 3.40 10

7.35 10 1023 3.844 10 2.89 10

orbit

kg mmsorbit Earth s

kg mmsorbit Moon s

L mvr

L kg m

L kg m

Example Solution 3Next find the rotational angular momentum:

2

2

225

224 6 3325

222 6 2925

2

25.97 10 6.378 10 7.08 10

86164

27.35 10 1.7375 10 2.36 10

27.32 86400

rot

kg mrot Earth s

kg mrot Moon ss

day

L I MRT

L kg ms

L kg mdays

So, Lorbit-Moon>Lrot-Earth>Lorbit-Earth>Lrot-Moon