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
Worked example
Reveal
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(b) The kinetic energy is given by K=Iω2/2

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
![\[ \omega_f=\frac{I_i\omega_i}{I_f}=3\omega_i=\xmlInlineElement[\xmlAttr{}{target}{slides}]{http://www.ph.ed.ac.uk/aardvark/NS/aardvark-latex}{aardvark:reveal}{22.6} \; rad\; s^{-1} \]](mastermathpng-1.png)
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.
[B] Consequences
There are many profound consequences of the law of conservation of angular momentum. In particular it explains:
- how gyroscopes behave;
- why it’s easier to ride a bicycle with big wheels;
- how gymnasts, divers and trapeze artists somersault;
- the shape of the solar system;
- why neutron stars and black holes rotate so fast.
- children’s toys !
Learning Resources
![]() | HRW Chapter 11.11-11.12 has many good examples. |
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