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Rotational Inertia & Angular Momentum

Rotational Inertia & Angular Momentum. 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 Momentum

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  1. Rotational Inertia & Angular Momentum

  2. 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)

  3. 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)

  4. 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 object’s rotation

  5. 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

  6. 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?v=w8Tfa5fHr3s

  7. 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

  8. Other Examples: Splash! Time Warp: Optimal Dive Spinning in zero Gravity

  9. 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.

  10. Momentum 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

  11. 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 angularmomentum of that system is conserved

  12. 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 ω -represents angular speed

  13. 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:

  14. Examples: • Helicopter tail rotor failure • Tail rotor failure #2

  15. Sports Connection… • 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)

  16. 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

  17. 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

  18. Applications… • The Big Cheese! • The Gyrowheel

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