Download Rotational Inertia and Angular Momentum

Rotational Inertia and
Angular Momentum
Inertia
• The resistance of
an object to
change its state of
motion
• Depends on mass
(the bigger the
mass, the bigger
the inertia).
Rotational Inertia
• The resistance of an object to change its
state of rotation
• Depends on the distribution of mass: the
further the mass is from the axis of rotation,
the more rotational inertia
vs
vs
Why do some racing bicycles
have solid wheels?
vs
• Which has more rotational inertia,
a spoke wheel or a solid wheel?
• Why?
Which has more rotational
inertia?
• Spoke wheel has more rotational inertia
because mass is distributed farther from
axis of rotation.
• Harder to start and stop rotating than solid
wheels.
Rotational Inertia Application
• Tight rope walkers
typically carry long
poles with lots of mass
on the ends.
• Why?
Rotational Inertia Wrap Up
• Mass is further from
the axis of rotation.
• An object will have
_______ rotational
inertia.
• It will be _______ to
rotate.
• It will be _______ to
balance.
• Mass is closer to the
axis of rotation.
• An object will have
_______ rotational
inertia.
• It will be _______ to
rotate.
• It will be _______ to
balance.
Force vs. Torque
• Force causes things to
accelerate.
• If you want something
to accelerate, apply a
force.
• F = ma
• Units: Newtons (N)
• Torque causes things
to rotate.
• If you want something
to rotate, apply a
torque.
• Torque =
perpendicular force x
lever arm
• Units: mN or Nm
Torque
For example: Let’s say
you are opening a door.
Loosening a bolt
• To get a bolt to turn you must apply a torque to
it.
• Describe a few different ways force a bolt to
turn.
Some torque
more torque,
Even more torque,
____________
____________
Torque & dragsters
• In terms of torque, why do dragsters have really
big back tires?
Torque and Balancing
• If a teeter-totter is
balanced, that means that
the torque on both sides is
equal but in the opposite
direction.
• A common mistake is that
students think the force is
the same on both sides but
that is not true. THE
TORQUE MUST BE THE
EQUAL!
Torque Practice Problem
F =?
40 kg
• A 40 kg child sits 1.5 meters away from the
center of a teeter-totter. How much force does
his dad need to exert 2 meters from the center
(on the other side) to prevent the child from
moving?
Angular Momentum
• Linear Momentum = mass x velocity
( p = mv )
• Angular Momentum =
rotational inertia x angular speed
Conservation of Angular
Momentum
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Why do ice skaters spin so much faster when they bring
their arms close to their bodies?
Conservation of Angular
Momentum
To understand why ice skaters, divers, & gymnasts
spin faster when they bring their bodies in we must
discuss the Conservation of Angular Momentum.
Law of Conservation of Angular
Momentum
• If no external torque acts on a rotating
system, the angular momentum of that
system is constant.
Angular Momentum Before = Angular Momentum After
Rot. Inertia x Rot. Velocity = Rot. Inertia x Rot. Velocity
(before)
(after)
big rotational inertia
small rotational velocity
small rotational inertia
big rotational velocity
The Angular Momentum for both is the same because
they have to be the same…IT’S A LAW!
Angular Momentum and Vectors
Angular Momentum like linear momentum
is a vector.
• What does that mean?
Direction is important!
The Direction of Angular
Momentum
Because the direction of something rotating is hard
to determine, physicists say that the direction of
angular momentum is in the plane of the rotation.
If this wheel was rotating, we would
say its angular momentum is pointed
in this direction.
So it would want to stay rotating in
that direction.
Examples of Angular Momentum
So next time you play:
- Football
- Frisbee
- Ride your bike
Remember you are just conserving angular
momentum.