Angular Momentum of Multiparticle Systems
The angular momentum principle may be extended to a multiparticle system to provide various insights.
The Main Idea
A Mathematical Model
The derivation of the angular momentum principle of a multiparticle system is most easily understood when following a simple example, in this case we will work with a three particle system:
- The angular momentum principle is written for each individual particle relative to location A, with position vectors r and external force vectors F.
- The individual equation is then summed. Note that, due to the reciprocation of forces, the internal forces f cancel out.
- The equation is now rewritten with the right side, representing net torque, as τnet,A
A Computational Model
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
Difficult
Each of the six particles in the figure have identical mass m and moves in the x-y plane with the same speed v as indicated in the diagram. Take the location of particle 5 as the reference point for all angular momentum calculations when answering the following questions.Be sure to express your answer as a vector.
- What is the momentum of the individual particles?
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