Angular Momentum of Multiparticle Systems

The angular momentum principle may be extended to a multiparticle system to provide various insights.

Main Idea

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 τ_net,A

Computational Model

Glowscript Trinket Example

Examples

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?

Consider the particles above as a single multiparticle system. With respect to particle 5, what is the total angular momentum of the system? What is the translational angular momentum? What is the rotational angular momentum?

Connectedness

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History

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See also

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External links

The Momentum Principle in Multi-Particle Systems (Video)

Angular momentum of a multi-component system

Chapter 5: Systems of particles, Dynamics Lecture Notes, University of Cambridge Department of Applied Mathematics and Theoretical Physics

Chapter 19 Angular Momentum, MIT Course Materials

[http://www.rakeshkapoor.us/ClassNotes/classnotes.php?notes=TorqueAndAngularMomentum&index=1 Torque and Angular Momentum General Physics (calculus based) Class Notes Dr. Rakesh Kapoor, M.Sc., Ph.D. Former Faculty-University of Alabama at Birmingham]

References

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