Angular Momentum of Multiparticle Systems: Difference between revisions

Revision as of 03:17, 5 December 2015

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

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?

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?

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History

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References

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 Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?
-===Further reading===
+===External links===
+[http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-Particle Systems (Video)]
+[http://farside.ph.utexas.edu/teaching/301/lectures/node120.html Angular momentum of a multi-component system]
-Books, Articles or other print media on this topic
+[http://www.damtp.cam.ac.uk/user/stcs/courses/dynamics/lecturenotes/section5.pdf Chapter 5: Systems of particles, Dynamics Lecture Notes, University of Cambridge Department of Applied Mathematics and Theoretical Physics]
-===External links===
+[http://web.mit.edu/8.01t/www/materials/modules/chapter19.pdf Chapter 19 Angular Momentum, MIT Course Materials]
-[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]
+[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==