PHYSICS 231 Lecture 20: Angular momentum

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PHYSICS 231Lecture 20 Angular momentum
Neutron star

• Remco Zegers
• Walk-in hour Thursday 1130-1330 am
• Helproom

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In the previous episode..
??I? (compare to ?Fma) Moment of inertia I
I(?miri2) ? angular acceleration I depends on
the choice of rotation axis!!
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Rotational kinetic energy
KEr½I?2
Conservation of energy for rotating
object PEKEtKErinitial PEKEtKErfinal
Example.
1m
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Angular momentum
Conservation of angular momentum If the net
torque equal zero, the angular momentum L does
not change Ii?iIf?f
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Conservation laws

• In a closed system
• Conservation of energy E
• Conservation of linear momentum p
• Conservation of angular momentum L

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Neutron star
Sun radius 7105 km
Supernova explosion
Neutron star radius 10 km
Isphere2/5MR2 (assume no mass is
lost) ?sun2?/(25 days)2.910-6
rad/s Conservation of angular momentum Isun?sun
Ins?ns (7E05)22.9E-06(10)2?ns ?ns1.4E04
rad/s so period Tns5.4E-04 s !!!!!!
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The spinning lecturer
A lecturer (60 kg) is rotating on a platform with
?2? rad/s (1 rev/s). He is holding two masses
of 0.8 m away from his body. He then puts the
masses close to his body (R0.0 m). Estimate how
fast he will rotate.
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2001 a space odyssey revisited (lec. 16, sh. 12)
A spaceship has a radius of 100m and I5.00E8
kgm2. 150 people (65 kg pp) live on the rim and
the ship rotates such that they feel a
gravitational force of g. If the crew moves to
the center of the ship and only the captain
would stay behind, what gravity would he feel?
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The direction of the rotation axis
L
The rotation in the horizontal plane is reduced
to zero There must have been a large net torque
to accomplish this! (this is why you can ride a
bike safely a wheel wants to keep turning in the
same direction.)
The conservation of angular momentum not only
holds for the magnitude of the angular momentum,
but also for its direction.
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Rotating a bike wheel!
A person on a platform that can freely rotate is
holding a spinning wheel and then turns the
wheel around. What will happen?
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Demo defying gravity!
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Global warming
The polar ice caps contain 2.3x1019 kg of ice. If
it were all to melt, by how much would the length
of a day change? Mearth6x1024 kg Rearth6.4x106 m
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Two for the weekend...
What is the tension in the tendon?
30N
12.5N
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A top
A top has I4.00x10-4 kgm2. By pulling a rope
with constant tension F5.57 N, it starts to
rotate along the axis AA. What is the angular
velocity of the top after the string has been
pulled 0.8 m?