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?
Answer
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.
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