Rotational inertia angular momentum
1 / 19

Rotational Inertia & Angular Momentum - PowerPoint PPT Presentation

  • Uploaded on

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 ).

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about ' Rotational Inertia & Angular Momentum ' - jewell

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Inertia linear quantity
Inertia (linear quantity)




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)




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


    • 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


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:


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.






  • 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





  • 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:


  • 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



    • 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


  • The Big Cheese!

  • The Gyrowheel