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I wonder if there is a meaning of rotation for a point particle. Does a point particle have angular momentum and does he reply to torque?

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  • $\begingroup$ Hi David. The term circular motion means moving in a circle and point particles can of course move in a circle. Do you mean rotation i.e. can a point particle rotate? $\endgroup$ – John Rennie May 17 '19 at 10:58
  • $\begingroup$ yes that's what I mean.. sorry for that $\endgroup$ – david May 17 '19 at 11:02
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    $\begingroup$ Hi david: Welcome to Phys.SE. Are you talking about a purely classical point particle, or are you also allowing internal quantum spin of the point particle? $\endgroup$ – Qmechanic♦ May 17 '19 at 11:55
  • $\begingroup$ hey, I'm talking about purely classical point particle $\endgroup$ – david May 17 '19 at 12:05
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The one-word answer is "no".

Consider a cube with side $a$ made of material with density $\rho$. The mass of the cube is $\rho a^3$. The moment of inertia about the center is $\rho a^5/6$.

As $a \to 0$, the moment of inertia gets smaller much faster than the mass, because of the $a^5$ factor compared with $a^3$.

Another way to see this is to think about the rotational inertia of a uniform rod of length $l$. You can find the moment of inertia about the center by the "standard" formula, or you can cut the rod into $n$ equal pieces and find the moment of inertia using the parallel axis theorem. If you do that, you find that as $n$ increases, the contribution from the moment of inertia of each piece about its own center is negligible compared with the "$\text{mass}\times\text{length}^2$" contributions from the parallel axis theorem. So as $n \to \infty$ the moment of inertia of each piece (i.e. each "point particle") about its own center is $0$.

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  • $\begingroup$ so a point particle can't rotate itself, and therefore can't have angular momentum in this specific situation. but a point particle can rotate around another point particle and therefore he can have angular momentum in this case? $\endgroup$ – david May 17 '19 at 15:04

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