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

PHY221 Ch19/20 : Angular Momentum1.

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n Po

ints

Definition of: or for N particles:

Proof:

L r p ������������������������������������������

1

N

i ii

L r p

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dL

dt

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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!

PHY221 Ch19/20: Angular Momentum1.

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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)

PHY221 Ch19/20 : Angular Momentum2.

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Example: Person jumps on merry-go-round: given m, M and vo what is the final w of person +merry-go-round

PHY221 Ch19/20 : Angular Momentum2.

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Example: Skater

PHY221 Ch19/20 : Angular Momentum2.

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Example: Planet around Sun. Prove conservation of L by showing t=0

PHY221 Ch20: Angular Momentum2.

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Example: Mass pulled by a central string

Energy consideration when string is pulled in:

Torque and angular momentum:

PHY221 Ch20: Angular Momentum2.

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Example: Perpendicular and L L precession

Gyroscope: start with spinning top held at both ends and remove one end:

𝐿 𝜏

𝜔

PHY221 Ch19: Angular Momentum2.

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