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I'm aware similar questions have been asked, but I didn't understand the answers.

  • Can a particle experience torque?
  • What about angular velocity and/or acceleration?

Assuming a particle is a body where all the mass is concentrated at a single point in space, then torque would be: $\Sigma\tau=F_\perp R$, where $R\to0$, meaning $\Sigma\tau\to0$. Therefore, from my understanding, particles can't experience torque. However, I know they are able to possess angular momentum.

  • How would a particle have angular momentum if it can't experience torque?
  • Conversely, is my understanding at fault, and particles are indeed able to experience torque?

Thank you so much for the help.

Similar Questions:

nebbie
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2 Answers2

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Assuming a particle is a body where all the mass is concentrated at a single point in space, then torque would be: Σ=⊥, where →0, meaning Σ→0. Therefore, from my understanding, particles can't experience torque. However, I know they are able to possess angular momentum.

Torque is just the "thing" that causes a change in angular momentum. So if a particle can have angular momentum $L_0$ and later $L_1$ with the two not equal, it has experienced a torque.

You have shown that a point particle cannot have rotational angular momentum (and cannot experience torque that changes the rotational angular momentum). But it can have angular momentum from motion about another point.

$L = mvr \sin(\theta)$ or $L = \vec{r} \times \vec{p}$. Changing the velocity of the particle in a way that changes the quantity can be considered a torque in this context.

Angular momentum of a particle

BowlOfRed
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Torque and angular momentum are defined with respect to a point.

So, if you stand with an outstretched arm on a turntable and catch a baseball thrown off axis, you will turn when you catch the baseball. That baseball had angular momentum about the axis of the turntable, some of which was transferred to you.

robphy
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  • Yes, I understand the concept of angular momentum. An arm is able to spin when it catches a ball because it has a length.

    I'm trying to understand how a particle with no size would spin.

    Could you elaborate on the part about torque/angular momentum being defined with respect to a point?

     – nebbie Aug 19 '22 at 20:05
  • @nebbie Where is the tail of the $\vec r$-vector when writing $\vec\tau=\vec r \times \vec F$ and $\vec L=\vec r \times \vec p$? – robphy Aug 19 '22 at 20:14