Angular Momentum

Section 9.7

Definition of Angular Momentum

First – definition of torque:

τ = Frsinθ

the direction is either

clockwise or counterclockwise

a net torque produces a change in ang. Motion

Simulation - Two torques acting on a wheel

F

Angular Momentum

sinl mvr

l mv r

ExampleRank the following from largest to smallest angular momentum.

answer

Review Important Ideas

Angular Velocity = Angular Displacement/time

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.

t

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.

Orbit of planets and Blocks on a rotating rod

sinl mvr

ExampleThe figure below shows two masses held together by a thread on a rod that is rotating about its center with angular velocity, ω. If the thread breaks, what happens to the system's (a) angular momentum and (b) angular speed. (Increase, decrease or remains the same)

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

ExampleFour 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.

1.2 m

2.5 kg

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