# Angular momentum free particle problem

1. Aug 16, 2014

### rtsswmdktbmhw

1. The problem statement, all variables and given/known data
'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.'

2. Relevant equations
$\frac{d\vec{l}}{dt}=∑\vec{\tau}$
$\vec{l}=\vec{r}\times\vec{p}$

3. 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.

2. Aug 16, 2014

### CAF123

...
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.

3. Aug 16, 2014

### rtsswmdktbmhw

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

Thanks for pointing that out to me :)