Angular Momentum of Multiparticle Systems: Difference between revisions
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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? | Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context? | ||
=== | ===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] | |||
[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] | |||
[http://web.mit.edu/8.01t/www/materials/modules/chapter19.pdf Chapter 19 Angular Momentum, MIT Course Materials] | |||
[http:// | |||
[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== | ==References== |
Revision as of 02:17, 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 τnet,A
Computational Model
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?
Connectedness
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- How is it connected to your major?
- Is there an interesting industrial application?
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 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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