PHYS 1441 – Section 501
Lecture #14
Wednesday, July 21, 2004
Dr. Jaehoon Yu
•
•
Angular Momentum and Its Conservation
A table of angular and linear quantity comparisons
Today’s homework is #7, due 6pm next Wednesday, July 28!!
Wednesday, July 21, 2004
PHYS 1441-501, Summer 2004
Dr. Jaehoon Yu
1
Announcements
• Term2 exam results
– Average: 63.8
– Top score: 94
– How did you do in term 1?
• 60.9
• 2nd quiz next Monday, Aug. 2
– Section 8.6 – whatever we cover till next Wednesday
• Final term exam Wednesday, Aug. 11
– Covers: Section 8.6 – wherever we cover by Aug. 4
– Review on Aug. 11
• We will go through the exam problems together and will
have individual discussions on how you could improve
Wednesday, July 21, 2004
PHYS 1441-501, Summer 2004
Dr. Jaehoon Yu
2
Conservation of Angular Momentum
Remember under what condition the linear momentum is conserved?
Linear momentum is conserved when the net external force is 0.  F  0 
dp
dt
p  const
By the same token, the angular momentum of a system
is constant in both magnitude and direction, if the
resultant external torque acting on the system is 0.
What does this mean?
dL


ext
0

dt
L  const
Angular momentum of the system before and
after a certain change is the same.
ur
ur
L i  L f  constant
Three important conservation laws
for isolated system that does not get
affected by external forces
Wednesday, July 21, 2004
Ki  U i  K f  U f
ur
ur
pi  p f
ur
ur
Li  L f
PHYS 1441-501, Summer 2004
Dr. Jaehoon Yu
Mechanical Energy
Linear Momentum
Angular Momentum
3
Example for Angular Momentum Conservation
A star rotates with a period of 30days about an axis through its center. After the star
undergoes a supernova explosion, the stellar core, which had a radius of 1.0x104km, collapses
into a neutron start of radius 3.0km. Determine the period of rotation of the neutron star.
What is your guess about the answer?
Let’s make some assumptions:
Using angular momentum
conservation
The period will be significantly shorter,
because its radius got smaller.
1. There is no torque acting on it
2. The shape remains spherical
3. Its mass remains constant
Li  L f
I i  I f  f
The angular speed of the star with the period T is
Thus

Tf 
I i
mri 2 2


f
If
mrf2 Ti
2
f
 r f2
 2
r
 i
Wednesday, July 21, 2004
2

T
2

3
.
0


6
Ti  

2
.
7

10
days  0.23s

30
days

4

1
.
0

10



PHYS 1441-501, Summer 2004
Dr. Jaehoon Yu
4
Similarity Between Linear and Rotational Motions
All physical quantities in linear and rotational motions show striking similarity.
Quantities
Mass
Length of motion
Speed
Acceleration
Force
Work
Power
Momentum
Kinetic Energy
Wednesday, July 21, 2004
Linear
Mass
M
Distance
r
t
v
a
t
L
v
I  mr 2
Angle  (Radian)

t


t

P  F v
Torque   I
Work W  
P  
p  mv
L  I
Force F  ma
Work W  Fd cos
Kinetic
Rotational
Moment of Inertia
K
1
mv 2
2
PHYS 1441-501, Summer 2004
Dr. Jaehoon Yu
Rotational
KR 
1
I 2
2
5