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Action is defined as:

$$ S = \int_{t_1}^{t_2} L dt,$$

And has units of joule-second. Angular momentum has the same units, but has a completely different application and interpretation. Are there any similarities between the Action and Angular momentum? Is there a way to compare them or are they both applications of something more general.

Are there situations where you have to use calculus of variations to minimize the angular momentum for a physical situation?

Qmechanic
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bananenheld
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  • We know that in rotational motion, a body tries to have kinetic energy it gains through external force, but that is restricted by centripetal force. Reason is that molecular structure of a body keeps it shape or position. So there is minimum action and body start to rotate. Also body wants to keep its speed once gain. – Neil Libertine Dec 04 '22 at 08:36
  • Possible duplicates: https://physics.stackexchange.com/q/28957/2451 and links therein. – Qmechanic Dec 04 '22 at 08:47
  • @Neil Libertine thank you for your response, could you maybe expand to that? – bananenheld Dec 04 '22 at 10:37
  • Dimensional analysis is analogous to casting out nines. Going down to a tally of the dimensions means you go to a much smaller space. There is no ground to propose that Action $S$ and angular momentum $L$ ending up in the same bin in terms of their dimensions carries significance. – Cleonis Dec 04 '22 at 13:38
  • @bananenheld A point on a rotating rigid body is experiencing centripetal force yet not collapsed to centre. That means it holds lagrangian to be minimum and all that force converts into kinetic energy and keeps angular momentum constant. – Neil Libertine Dec 04 '22 at 13:48

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