Conservation of Angular Momentum C13, C14

Basic Definitions… Torque (finally we get some direction!) Use the Right-Hand-Rule to determine the direction of Torque. Curl the fingers of your right hand in the same direction that the object spins - your thumb points in the direction of the angular velocity, angular momentum, torque, acceleration, displacement …. Use VPython as a “vector calculator”!

Basic Definitions… Angular Momentum Note the fundamental link to the linear world in this form of the expression for angular momentum

In other words... Angular Momentum can be thought of in many different ways: These all inter-relate and each equation illustrates an aspect of this fundamental idea

Conservation of Angular Momentum Just as a moving object has linear momentum - a spinning object possesses angular momentum. As long as there are no external torques and the object is in an isolated system, angular momentum is conserved.

Examples of Conservation of Angular Momentum The figure skater – just Physics? Watch for the relationship between: –Arm movement and rotational speed –Rotational speed and vertical stability

Examples of Conservation of Angular Momentum The following applet can be used to illustrate conservation of L Neutron stars and PULSARS are nature’s version of the previous two examples! PULSARS

Angular Momentum and Precession What happens if we try to spin an object that is already spinning? Answer: depending how we do it the result can be counter- intuitive Go to VPython simulation

Digging Deeper – the math behind precession The slow rotation of a spinning wheel, suspended at only one point is an example of precession. We can easily determine the precession rate:

re-arrange to give… Example: a 1 kg bicycle wheel of radius 30 cm and spinning at 2 rev/s is suspended from a point 4 cm from the center of the wheel. What is the precession rate?

Important application - MRI