More Conservation Laws Linear Momentum

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More Conservation LawsLinear Momentum Angular
Momentum
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Linear Momentum

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The Fullback Scores

• by charging at the defence to drive into the
  endzone.
• His linear momentum is given by his
• mass x velocity

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It is Conserved!

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Where Does It Come From?
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Energy is Also Conserved(as we learned earlier)
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Angular Momentum

• Likewise a measure of momentum the product of
  mass x velocity
• But includes an element of turning or rotation

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So for a particle moving in a circular path

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For Extended Objects

• Simply add up the
• contributions from
• all the particles
• (atoms, etc), each
• in its own location
• relative to the axis
• of the motion

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Rotation vs Revolution - a Semantic Point

• A skater rotates (spins) around an axis, and the
  Earth rotates (spins) daily on its axis.
• But the Earth revolves around the sun (rotating
  as it does so!)

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Angular Momentum is Conserved(watch Daves
demonstrations)

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An Important ConsequenceThis Conservation
Yields Stability

• Frisbees footballs
• Rifle bullets
• Riding a bike

• Alexs diabolo
• The spin of the Earth!

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Where Does it Come From?

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Other Examples

• Dave on the piano stool
• The quarterback
• The human population as a circus bear

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Back to the Seasons

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The Important Ingredients

• The Earth is tipped a little relative to the
  plane of its orbit and
• Its spin axis stays pointing in the same
  direction as it orbits. (Conservation of Angular
  Momentum!) It does not flop about.

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But Slow Changes

• The axis of the Earth will point close to Polaris
  for many centuries
• -- but it does slowly change (precess) because
  of the tiny gravitational tugs of Jupiter and
  other objects.

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The Long-Term Result

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One More Consequence

• The days have a constant duration because the
  Earth cannot slow down or speed up dramatically.
• (We will learn later that the days are gradually
  lengthening thanks to the moon and the tides
  external influences.)

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Occasional Fluctuations

• the Indonesian earthquake decreased the length
  of day by 2.68 microseconds. Physically this is
  like a spinning skater drawing arms closer to the
  body resulting in a faster spin.