Transcript Angular Momentum

Angular Momentum
Chapter 11
Definition of Angular Momentum
First – definition of torque:
τ = Frsinθ
F
the direction is either
clockwise or counterclockwise
a net torque produces a change in ang. Motion
Simulation - Two torques acting on a wheel
Angular Momentum
l  mvr sin 
l  mv r
Example
Rank the following from largest to smallest
angular momentum.
answer
Review Important Ideas
Angular Velocity = Angular
Displacement/time


t
Just as it takes a impulse (force applied over
a time, FΔt) to change the momentum an
object, it takes an angular impulse (torque
applied over a time, τ Δt ) to change an
object's angular momentum.
The Conservation of Angular
Momentum
If no net external torques act on a system then
the system’s angular momentum, l, remains
constant. Speed and radius can change just as
long as angular momentum is constant.
l  mvr sin 
Examples of the Conservation of
Angular Momentum
Natalia Kanounnikova World Record Spin 308 RPM
Diving
18 meter high dive
Amazing Fouette Turns on Pointe
Playground Physics
Example
Four identical masses
rotate about a common
axis, 1.2 meters from the
center. Each mass is 2.5
kg, and the system rotates
at 2 rad/sec. The rods
connecting them are
assumed to be massless.
Find the total angular
momentum of this system.
2.5 kg
1.2 m
Answer
90.5 kg m2/s
Example Continued
The four masses are then pulled toward the
center until their radii are 0.5 meters. This is
done in such a manner that no external
torque acts on the system. What is the new
angular speed of the system?
36.2 rad/s