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

Angular Momentum

Example Rank 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.

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

Example The 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

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. 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