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Rotational Inertia & Angular Momentum

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Rotational Inertia & Angular Momentum

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)

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)

- 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

- Objects that are rotating about an
- A torque is required to change the status of an object’s rotation

- 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

- 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?v=w8Tfa5fHr3s

- Running
- When you run you bend your legs to reduce your rotational inertia

- Gymnastics/Diving
- Pull body into tight ball to achieve fast rotation

Splash!

Time Warp: Optimal Dive

Spinning in zero Gravity

- 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.

Symbol

Definition

Equation

Conservation

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

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 angularmomentum of that system is conserved

- 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

ω -represents angular speed

- 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:

- Helicopter tail rotor failure
- Tail rotor failure #2

- Ice skating
- Skater starts out in slow spin with arms and legs out
- http://www.youtube.com/watch?v=AQLtcEAG9v0
- http://www.youtube.com/watch?v=NtEnEeEyw_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)

- 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

- 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

- The Big Cheese!
- The Gyrowheel