rotational inertia & angular momentum. inertia (linear quantity) symbol definition limitations...
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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)
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)
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.) 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?
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
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:
Spinning in zero Gravity
Splash!
Time Warp: Optimal Dive
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
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
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 angular momentum of that system is conserved
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 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:
Helicopter tail rotor failure Tail rotor failure #2
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?
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
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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…
The Big Cheese!
The Gyrowheel