Rotational Inertia & Angular Momentum

1. Rotational Inertia & Angular Momentum

2. Rotational Inertia(I) • The resistance to 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 • Inertia depends on mass • Torque is required to change the status of an object’s rotation. It’s the rotational equivalent to force

3. LINEAR vs. ROTATIONAL • For every type of linear quantity we have a rotational quantity that does much the same thing Linear Quantities Speed Force Mass Momentum Distance Rotational Quantities Rotational (Angular) Speed Torque Rotational Inertia Angular Momentum Angle

4. Rotational Inertia (cont.) • Objects with mass closer to axis of rotation are easier to rotate, b/c it has 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

5. SUMMARY • 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.

7. Angular Momentum • Angular momentum is the “inertia of rotation” • Ang. Momentum= Rotational Inertia X Rotational Speed • Like normal momentum, but exclusively for rotation For you youngsters, an RPM is rotation per minute and we use to play records on a turn table. (stone age music)

8. 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

9. Sports Connection… • Ice skating • Skater starts out in slow spin with arms and legs out • http://www.youtube.com/watch?v=AQLtcEAG9v0 • Skater pulls arms and legs in tight to body • Skater is then spinning much fast (higher rotational speed) • Gymnastics/Diving • Pull body into tight ball to achieve fast rotation

10. It’s DEMO time!!!