Rotational inertia angular momentum
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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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Rotational inertia angular momentum

Rotational Inertia & Angular Momentum


Inertia linear quantity

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)


Rotational inertia angular equivalent

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)


Rotational inertia i

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


Rotational inertia cont

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


Why does a tightrope walker carry a long pole

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


Sports connection

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


Other examples

Other Examples:

Splash!

Time Warp: Optimal Dive

Spinning in zero Gravity


The big idea

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.


Momentum

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


Angular momentum

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


Conservation of angular momentum

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


Angular momentum1

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:


Examples

Examples:

  • Helicopter tail rotor failure

  • Tail rotor failure #2


Sports connection1

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)


Do cats violate physical law

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


Universe connection

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


Applications

Applications…

  • The Big Cheese!

  • The Gyrowheel


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