# Angular momentum and Rotation

Is Rotation a necessary condition for angular momentum? I mean can two bodies under translational motion in particular directions have a total angular momentum that is not zero?

You do not have to have rotation to have angular momentum. And you do not have to have two bodies.

One body moving with constant speed in a straight line has nonzero angular momentum around any point not on that line!

In Newtonian physics, angular momentum is $$\mathbf{r}\times\mathbf{p}$$. It is much more general than something involving circular orbits or rotating objects. And it is just as important as the momentum $$\mathbf{p}$$ because it is conserved just like $$\mathbf{p}$$ is.

Angular momentum is defined as $$\vec {L}= \vec {r} \times \vec {P}$$ if the velocity of the object is in the same direction with position vector then angular momentum would be zero.

Or in another perspective we can write in the abive equation like

$$L=rPsin(\theta)$$ or in magnitude

$$L=rmvsin(\theta)$$

So, there has to be some angle between $$\vec{r}$$ and $$\vec{v}$$. Otherwise the result becomes zero.

The electron has angular momentum (spin) and being a point particle saying it rotates about its axis is a meaningless statement.

Please note that angular momentum is not a quantity that stands on its own, but rather it designates that there is linear momentum at a distance from where it is measured. The formula of the moment of momentum (angular momentum) is

$$\vec{L} = \vec{r} \times \vec{p}$$

This is entirely analogous to the relationship between torque and force. Torque is an indication of a force at a distance from where it is measured. The formula of the moment of force (torque) is

$$\vec{\tau} = \vec{r} \times \vec{F}$$

The law of conservation of angular momentum is not entirely separate from the law of conservation of momentum. Rather it indicates that not only momentum is conserved in magnitude and direction, but also the line of action of momentum (axis of percussion) is conserved in space.

In summary, a single particle moving along a path with non-zero momentum will have measured angular momentum away from the path, just as a force applied tangentially will have a torque measured away from the path.