phy221 ch19/20: angular momentum 1.main points: definition proof dl/dt= proof l=i for a rigid body...
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![Page 1: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/1.jpg)
PHY221 Ch19/20: Angular Momentum
1. Main Points: • Definition• Proof dL/dt=• Proof L=I for a rigid body• Conservation of L
2. Examples• Person running and jumping on merry-go-round• Skater• Gravity on Planet Sun
![Page 2: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/2.jpg)
PHY221 Ch19/20 : Angular Momentum1.
Mai
n Po
ints
Definition of: or for N particles:
Proof:
L r p ������������������������������������������
1
N
i ii
L r p
������������������������������������������
dL
dt
��������������
Follow parallel with introduction of momentum in translational description:
As before we’ll only consider motion in a plane and thus all rotational quantities are vectors along same direction which is the axis perpendicular to that plane => we don’t worry about vectors!
![Page 3: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/3.jpg)
PHY221 Ch19/20: Angular Momentum1.
Mai
n Po
ints
Proof of L=I for a rigid body (I =constant) by using = I
Conservation of L when no external torque
We assume internal Action/Reaction forces to act on the same line (not just direction)
![Page 4: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/4.jpg)
PHY221 Ch19/20 : Angular Momentum2.
Dis
cuss
Example: Person jumps on merry-go-round: given m, M and vo what is the final w of person +merry-go-round
![Page 5: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/5.jpg)
PHY221 Ch19/20 : Angular Momentum2.
Dis
cuss
Example: Skater
![Page 6: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/6.jpg)
PHY221 Ch19/20 : Angular Momentum2.
Dis
cuss
Example: Planet around Sun. Prove conservation of L by showing t=0
![Page 7: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/7.jpg)
PHY221 Ch20: Angular Momentum2.
Dis
cuss
Example: Mass pulled by a central string
Energy consideration when string is pulled in:
Torque and angular momentum:
![Page 8: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/8.jpg)
PHY221 Ch20: Angular Momentum2.
Dis
cuss
Example: Perpendicular and L L precession
Gyroscope: start with spinning top held at both ends and remove one end:
𝐿 𝜏
𝜔
![Page 9: PHY221 Ch19/20: Angular Momentum 1.Main Points: Definition Proof dL/dt= Proof L=I for a rigid body Conservation of L 2.Examples Person running and](https://reader030.vdocuments.mx/reader030/viewer/2022032612/56649ec05503460f94bcba4e/html5/thumbnails/9.jpg)
PHY221 Ch19: Angular Momentum2.
Dis
cuss