Transcript Rotational Inertia & Angular Momentum

ROTATIONAL INERTIA &
ANGULAR MOMENTUM
Inertia (linear quantity)
m (mass)
Symbol

Definition

Limitations

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
Depends on

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?
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

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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:
Splash!
Time Warp: Optimal Dive
Spinning in zero Gravity
The big idea


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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

p
Definition

Inertia in motion
Equation

Momentum = mass x velocity (p=mv)
Conservation

If no unbalanced external force acts on
an object, the momentum of that
object is conserved
Angular Momentum
Symbol

L
Definition

Inertia of rotation
Equation
Conservation


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
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

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?
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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
17
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…
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The Big Cheese!

The Gyrowheel