Angular momentum free particle problem

[rtsswmdktbmhw]

Homework Statement

'Consider an inertial frame in which a free particle travels past the origin O but does not go through it. Show by direct calculation that the particle's angular momentum about O is constant.'

Homework Equations

$\frac{d\vec{l}}{dt}=∑\vec{\tau}$
$\vec{l}=\vec{r}\times\vec{p}$

The Attempt at a Solution

I tried working backwards; if angular momentum is a constant then $\frac{d\vec{l}}{dt}=0$ so that the integral gives a constant. That would mean the angular momentum is conserved, but the question doesn't specify that the system is isolated or that there is only central forces acting which are the conditions for conservation.

Am I missing something obvious? I don't think this was meant to be a particularly challenging question.

 

[CAF123]

Homework Statement

'Consider an inertial frame in which a free particle...

...

the question doesn't specify that the system is isolated or that there is only central forces acting which are the conditions for conservation.

The 'free' in 'free particle' means that the particle is subject to no outside influences, so in particular no external forces and completely isolated.

I would suggest writing expressions for the angular momentum at two arbritary positions using the cross product definition and analyse the difference.

 

[rtsswmdktbmhw]

...


The 'free' in 'free particle' means that the particle is subject to no outside influences, so in particular no external forces and completely isolated.

Oh... derp. I feel silly for not knowing that. That makes the question so trivial now.

Thanks for pointing that out to me :)