Rotational Inertia

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Rotational Inertia Angular Momentum
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Rotational Inertia (I)

• Resistance to change in rotational motion
• Objects that are rotating about an axis tend to
  stay rotating, objects not rotating tend to
  remain at rest, unless an outside torque is
  applied
• A torque is required to change the status of an
  objects rotation
• Its the rotational equivalent to mass for linear
  problems

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• For every type of linear quantity we have a
  rotational quantity that does much the same thing

Linear Quantities Speed Force Mass Momentum Dista
nce
Rotational Quantities Rotational (Angular)
Speed Torque Rotational Inertia Angular
Momentum Angle
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Rotational Inertia (cont.)

• Some objects have more rotational inertia than
  others
• Objects with mass closer to axis of rotation are
  easier to rotate, b/c it they have less
  rotational inertia
• If the mass is farther away from the axis, then
  object will have more rotational inertia, and
  will therefore be harder to rotate

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Why does a tightrope walker carry a long pole?

• The pole is usually fairly heavy and by carrying
  it, he creates a lot of mass far away from the
  axis of rotation
• This increases his rotational inertia
• And therefore makes it harder for him to
  rotate/tip over

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Sports Connection

• Running
• When you run you bend your legs to reduce your
  rotational inertia
• Gymnastics/Diving
• Pull body into tight ball to achieve fast
  rotation

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The big idea

• Rotational Inertia depends on mass and radius
• If either one of these is large, then rotational
  inertia is large, and objectwill be harder to
  rotate
• Different types of objects have different
  equations for rotational inertia
• But all equations have m and r2 in them.

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Angular Momentum

• inertia of rotation
• Ang. Momentum Rotational Inertia X Rotational
  Speed
• Like normal momentum, but exclusively for rotation

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Conservation of Angular Momentum

• If no outside torque is being applied, then
  angular momentum must stay the same
• This means, if you decrease radius, you increase
  rotational speed
• Increase radius, then rotational speed decreases

I represents rotational inertia ? -represents
angular speed
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Sports Connection

• Ice skating
• Skater starts out in slow spin with arms and legs
  out
• Skater pulls arms and legs in tight to body
• Skater is then spinning much fast (higher
  rotational speed)
• Gymnastics (pummel horse or floor routine)
• Small radius to achieve fast rotational speed
  during moves, increase radius when low rotational
  speed is desired (during landing)

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Universe Connection

• Rotating star shrinks radius. What happens to
  rotational speed??
• Goes way up.. Spins very fast
• Rotating star explodes outward. What happens to
  rotational speed??
• Goes way down spins much slower
• Test on Friday!!! Over Chapters 10 11
  (COG, torque, balancing, etc.) start Studying