Leigh wrote:
| I am confused by this. The general definition of the angular momentum
| of a system of particles with respect to *any* point is given by your
| expression. It is only necessary that all the Ri be relative to that
| same point. The Vi are merely time derivatives of the Ri; they are not
| usually thought of as being related to an origin.
The rotational form of Newton's second law (Torque = dL/dt) is applicable to
some few special circumstances in addition to that which uses a single
inertial "origin" for the calculation of torques and the particle positions
and velocities in L (the angular momentum of the many particle sysytem).
In particular, one can use an accelerating origin, A, for the calculation of
torques, and the position vectors in L, if the velocities in L are
calculated relative to an inertial frame AND the velocity of A is
parallel/antiparallel to the velocity of the CM of the system.
Leigh further wrote:
| I dislike this use of "spin" and "orbital" nomenclature. Consider the
| example of two solar systems bound in orbit with one another (a binary
| stellar system) and you will see that the distinction is next to
| useless.
You can easily show the many situations where this distinction is useless.
I don't know where it started, but it is not uncommon and, of course, has
found widespresd use in atomic system descriptions. I also recall an
astronomy book ascribing our night and day experience to the earth's spin
angular momentum and the seasonal experience to the earth's orbital AM.