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S5.8 Angular momentum conservation

[A] Conservation law

Given Key Point 5.18, in the absence of any external torques, we conclude that angular momentum is conserved.

Key Point 5.20

Angular momentum conservation. If the net external torque acting on a system is zero, the angular momentum $\vec{L}$ of the system remains constant, no matter what changes take place within the system.

Worked example

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Worked example

A women stands on a rotating platform with angular speed ω=7.54rads-1; she holds two weights in her outstretched hands. The moment of inertia of the woman-weights-platform system about the rotation axis is Ii=6.0 kg m2. If she moves the weights towards her body so that If=2.0 kg m2, calculate

  • [(a)] The change in ω.
  • [(b)] The change in kinetic energy.

Solution

(a) Since angular momentum is conserved we have Li=Lf or Iiωi=Ifωf. Hence

\[ \omega_f=\frac{I_i\omega_i}{I_f}=3\omega_i=\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{22.6} \; rad\; s^{-1} \]
(b) The kinetic energy is given by K=Iω2/2

Ki=6.0×7.542/2=170.5 J

Kf=2.0×22.62/2=510.8J

The additional energy comes from the (biological work) done by the woman in pulling in her arms.

 

Demo

Demo

Demonstration of conservation of angular momentum on a rotating chair
 

[B] Consequences

There are many profound consequences of the law of conservation of angular momentum. In particular it explains:

Learning Resources

Textbook: HRW Chapter 11.11-11.12 has many good examples.
Course Questions:
Self-Test Questions: