Angular Momentum 2
• Angular momentum of a particle
Text sections 11.2 - 11.4
Chapter 11, problems 11, 13, 15, 19, 55
Two astronauts are held together by a long rope and rotate about
their common center of mass. One has twice the mass of other.
One astronaut gathers in 1/3 of the rope separating them.
Which of the following remains constant?
A) Kinetic energy
B) Angular velocity
C) Angular momentum
D) Tension in the rope
By what factor do each of the others change?
1 Angular momentum of a particle
L =r×p =r×(mv)
This is the fundamental definition of L.
• L is a vector. O
• Like torque, it depends on the choice
of origin (or “pivot”). x m φ
• If the particle motion is all in the x-y
plane, L is parallel to the z axis.
Angular momentum of a particle (2-D):
|L| = mrv⊥ r ⊥
= mvr sin φ , etc
For a particle travelling in a circle (constant |r|),
v ⊥ r ω, and
L = mrv ⊥ mr ω = Iω
2 A hockey puck slides in a straight line at constant speed past a
physicist at O. How does its angular momentum about O change
A) increases, then decreases
B) decreases, then increases
C) remains constant, but not zero O
D) is zero unless the puck is spinning
General motion: “orbital” and “spin” angular momentum
L =r×p =r