Chapter 11: Angular Momentum part 2
Reading assignment:
review for exam
Homework :
due Monday, Oct. 24, 2005 (an extra week to do it!)
Problems:
Q3, 1, 2, 3, 6, 9, 11, 14, 20, 36, 43
• Rolling motion (axis of rotation is moving)
• Torque
• Angular momentum
• Angular momentum is conserved
Angular momentum of a particle
Definition:
  
Lrp

 m(r  __)
L… _____________________
r… distance from the origin
p… momentum of __________
v…velocity of ______________
L is ____________ to r and p
L has magnitude L = ________
Angular momentum of a rotating
rigid object
We’ll consider an object that is
rotating about the _________.
The angular momentum of the
object is given by:
Lz  I  
Note that in this case L and  are along the _____________.
Also note the analog formula for _________ momentum p = m·v
Black board example 12.3
A light rigid rod, 1 m in length,
joins two particles – with
masses 3 kg and 4 kg at its end.
The system rotates in the x-y
plane about a pivot through the
center of the rod.
Determine the angular
momentum of the system about
the origin when the speed of
each particle is 5.00 m/s.
Conservation of angular momentum
The total angular momentum of a system is _____________
in both magnitude and direction if the resultant external
torque acting on the system is zero.

L  ____________
If the system undergoes an internal __________________ then:
 
Li  L f  ____________
If the object is rotating about a _______ axis (say z-axis), then:
I ii  I f  f  _____________
________________ laws
Ki  U i  K f  U f 

 
pi  p f
 For an isolated system
 

Li  L f

Demo
A students stands still on a rotatable platform
and holds a spinning wheel. The bicycle wheel is
spinning in the clockwise direction when viewed
from above.
He flips the wheel over.
What happens?
Black board example 12.4
HW 39
Student on a turn table.
A student stands on a platform that is rotating with an angular
speed of 7.5 rad/s, his arms outstretched and he holds a brick
in each hand. The rotational inertia of the whole system is 6.0
kg·m2. The student then pulls the bricks inward thus reducing
the rotational inertia to 2.0 kg·m2.
(a) What is the new angular speed of the platform?
(b) What is the ratio of the new kinetic energy of the system to
the original kinetic energy?
(c) What provided the added kinetic energy?