11/27 Angular Momentum

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11/27 Angular Momentum

• Begin Simple Harmonic Motion (SHM) Wednesday
• Exam IV Thursday Eve 12/5 5-7 Wit 116
• No class Monday!!!

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Angular Momentum

• uses the symbol L
• given by L I? (recall p mv)
• L conserved if net external torque 0(p
  conserved if net external force 0)

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Angular Momentum
Disk spinning on a frictionless axle. Any
external torque?
There are external forces, WE,D and NA,D, but
they do not produce any torque. Angular momentum
is conserved, (? doesnt change).
?
Yes, fH,D produces an external torque and the
angular momentum decreases.
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Angular Momentum L I?
Identical disks spinning in opposite directions
at the same angular speed.
The top disk falls down on the lower one. What
happens?
They both slow down and stop.
Are there external torques on the individual
disks?
Yes, one puts a torque on the other.
What if we consider the system of both disks?
No external torque (forces are internal now) and
the angular momentum of the system is conserved.
The total L initially is zero since they both
have the same Is and their ?s are opposite (but
equal). L initial L final
? ?
0
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Angular Momentum L I?
Now only one disk is spinning. What is the
initial angular momentum of the system?
1
2
What is the final angular momentum of the system?
?i
The same, no external torque.
What is the final angular speed of the system?
Both spinning at the same speed and...
?f ?
I doubles do ? is halved
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Angular Momentum L I?
Is rotational kinetic energy conserved?
KER,i 1/2I?i2
?i
KER,f 1/2(2I)(?i/2)2
1/4I?i2
Rotational kinetic energy is not conserved. This
is a completely inelastic collision.
?f ?
?i/2