Conservation of angular momentum

L I

A system of objects that experiences no external torques has a constant total angular momentum

initial finalL L

For a spinning object

Skater and spinning

A system of objects that experiences no external torques has a constant total angular momentum

total,initial total,finalL L

Suppose she can reduce her moment of inertia by a factor of 2. What happens to her w ?

What happens to her KE ?

Where does the KE come from?

An immense cloud of rotating gas and dust contracted under the influence of gravity to form the Earth and in the process rotational kinetic energy increased.

Where did this KE come from?

What was conserved?

Angular momentum of an object moving in a straight line?

Suppose I’m on a merry-go-round, and the ground is totally frictionless ice.

All I have is a machine gun. How can I get the M-G-R to turn?

Angular momentum of an object moving in a straight line!

For an object moving in a line

is the “moment arm” between the axis and the line of v.

L r mv

r

Angular momentum of an object moving in a straight line!

For an object moving in a line

is the distance between the axis and the line of v.

L rmv

r

P3. What can divers change after they leave the board? A. w B. L C. I D. L & I E: I & w

Gyros: If no external torques… the rotation axis (and L) points the same direction in space.

José sits on frictionless ice, holding a spinning bicycle wheel. Viewed from above it is going clockwise (CW). Call this direction +.

Total (wheel + José) angular momentum is conserved (including direction) P6. If he grabs on to the wheel edge firmly and “stops” it he will then beA. turning CW (viewed from the top)B. turning CCW C. not turning

José sits on frictionless ice, holding a spinning bicycle wheel. Viewed from above it is going clockwise (CW). Call this direction +.

Total (wheel + José) angular momentum is conserved (including direction) P6. If he grabs on to the wheel edge firmly and “stops” it he will then beA. turning CW (viewed from the top)B. turning CCW C. not turning

P7. If instead of stopping it he flips the wheel over, so it is going CCW (- direction) , he will be A. turning CW slower than in P4. B. turning CCW slower than in P4C. turning CW faster than in P4. D. turning CCW faster than in P4

Gravity

Classical physics was invented to understand motion of the planets

Newton’s thoughts about the moon’s orbit and projectile motion about 1670:

Parabola of projectile turns into a circle if the speed is just right

The apple, the moon and the cannonball are all doing the same thing…

They are all falling toward Earth’s center!

Universal law of gravity (Newton)

r is distance between centers of masses

2G

mMF G

r

G= 6.67 x10-11 Nm2/kg2 was found by experiment in 1783 by hanging masses!

Orbit relations:

2G

mMF G

r

g at the surface of any planet!

Where does g = 9.8 m/s2 come from?

The radius of a planet is about 1/3 that of Earth.Its mass is about 1/5 that of Earth. What is g on this planet?

Stars near center of our galaxy reveal black hole

3-D orbits reconstructed

http://science.nasa.gov/realtime/jtrack/3d/JTrack3D.html/