# Angular momentum in rotational motion

Ok so there are two things that have completely confused me- things related to angular momentum.

1.)First of all, how can a body possess angular momentum even though it is not rotating?

According to what I have read angular momentum is the rotational analogue of linear momentum.

2.)Plus, how can angular mometum be conserved in a certain situations but linear momentum be not?!?

Angular momentum is essentially the cross product of radius vector and linear momentum. Where have I gone wrong in understanding?

Thank You.

1.) Angular momentum is always with respect to a reference point. A massive particle moving in a straight line with momentum $\vec{p}$ will have angular momentum with respect to any point that is not on the worldline of the particle (since $\vec{r}$ and $\vec{p}$ will not be parallel, i.e. $\vec{r}\times\vec{p}\not=0$). Therefore, bodies can possess angular momentum without "rotating".
2.) When you compute the angular momentum $\vec{L}=\vec{r}\times\vec{p}$ the cross-product only takes into account the component of $\vec{p}$ which is orthogonal to $\vec{r}$, i.e. if a force acts on the body parallel to $\vec{r}$, the momentum will change but the angular momentum will not. Consider a planet orbiting a sun (in ideal circular motion). Then the gravitational force acts only parallel to the position vector when you compute the angular momentum of the planet with respect to the center of the sun. Therefore, the angular momentum with respect to this point will not change, but the momentum will constantly be changing direction and the angular momentum with respect to other points will change.