ROTATIONAL INERTIA & ANGULAR MOMENTUM

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 (sound familiar?)

Inertia depends on mass

Torque is required to change the status of an object’s rotation. It’s the rotational equivalent to force

LINERAR vs. ROTATIOANAL

For every type of linear quantity we have a rotational quantity that does much the same thing

Linear Quantities SpeedForceMassMomentumDistance

Rotational QuantitiesRotational (Angular) SpeedTorqueRotational InertiaAngular MomentumAngle

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

SUMMERY

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.

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)

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

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

It’s DEMO time!!!