Angular Momentum or Moment of Linear Momentum

In translational mechanics, the two central dynamical quantities are force and (linear) momentum $\vec{p}=m\vec{v}$. Rotational mechanics has an exact analogue of momentum too, called angular momentum (or 'moment of linear momentum', a name that hints directly at how it is built): if $\vec{p}$ is a particle's instantaneous linear momentum while it undergoes circular motion, its angular momentum at that instant, about the axis of rotation, is defined as $\vec{L}=\vec{r}\times\vec{p}$ where $\vec{r}$ is the position vector measured FROM the axis of rotation TO the particle. In magnitude, $L=pr\sin\theta$, where $\theta$ is the smaller angle between the directions of $\vec{p}$ and $\vec{r}$ -- i.e. L is the product of the linear momentum and its PERPENDICULAR distance from the axis of rotation. This is exactly parallel to how torque (the moment of a force) is built from a force and its perpendicular distanc …