Rotational Inertia

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Rotational Inertia Angular Momentum
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Inertia (linear quantity)

• Symbol
• Definition
• Limitations
• Depends on

• m (mass)
• An object at rest tends to stay at rest and an
  object in motion tends to stay in motion unless
• Acted upon by an outside force
• Mass (more mass more inertia)

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Rotational Inertia (angular equivalent)

• Symbol
• Definition
• Limitations
• Depends on

• I
• An object not rotating tends to stay not rotating
  and an object rotating about an axis tends to
  stay rotating about that axis unless
• Acted upon by an outside torque
• Mass distribution (more mass farther from axis of
  rotation more rotational inertia)

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Rotational Inertia(I)

• Inertia is a measure of laziness!
• Resistance to the 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

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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
• http//www.youtube.com/watch?vw8Tfa5fHr3s

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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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Other Examples
Splash!
Time Warp Optimal Dive
Spinning in zero Gravity
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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 object will 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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Momentum

• p
• Inertia in motion
• Momentum mass x velocity (pmv)
• If no unbalanced external force acts on an
  object, the momentum of that object is conserved

• Symbol
• Definition
• Equation
• Conservation

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Angular Momentum

• Symbol
• Definition
• Equation
• Conservation

• L
• Inertia of rotation
• Angular momentum rotational inertia x
  rotational velocity (L I )
• If no unbalanced external torque acts on a
  rotating system, the angular momentum of that
  system is conserved

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Conservation of Angular Momentum

• If no outside torque is being applied, then total
  angular momentum in a system 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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Angular Momentum

• The more rotational inetia has (the more mass
  farther out from the center) and the higher the
  rotational velocity, the more angular momentum it
  has. Example

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Examples

• Helicopter tail rotor failure
• Tail rotor failure 2

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Sports Connection

• Ice skating
• Skater starts out in slow spin with arms and legs
  out
• http//www.youtube.com/watch?vAQLtcEAG9v0
• http//www.youtube.com/watch?vNtEnEeEyw_s
• Skater pulls arms and legs in tight to body
• Skater is then spinning much faster (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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Do cats violate physical law?

• Video
• They rotate their tail one way, so that their
  body rotates the other so that their feet are
  facing the ground and they land on their feet.
• This combined with their flexibility allow them
  to almost always land on their feet

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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

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Applications

• The Big Cheese!
• The Gyrowheel