# Rotation of a Point Particle

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?

• 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? – John Rennie May 17 at 10:58
• yes that's what I mean.. sorry for that – david May 17 at 11:02
• 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? – Qmechanic May 17 at 11:55
• hey, I'm talking about purely classical point particle – david May 17 at 12:05

## 1 Answer

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 $$0$$.

• 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? – david May 17 at 15:04