  Angular momentum can be defined by rearranging the Komar surface integral in
terms of a twist form, encoding the twisting around of space-time due to a
rotating mass, and an axial vector. If the axial vector is a coordinate vector
and has vanishing transverse divergence, it can be uniquely specified under
certain generic conditions. Along a trapping horizon, a conservation law
expresses the rate of change of angular momentum of a general black hole in
terms of angular momentum densities of matter and gravitational radiation. This
identifies the transverse-normal block of an effective gravitational-radiation
energy tensor, whose normal-normal block was recently identified in a
corresponding energy conservation law. Angular momentum and energy are dual
respectively to the axial vector and a previously identified vector, the
conservation equations taking the same form. Including charge conservation, the
three conserved quantities yield definitions of an effective energy, electric
potential, angular velocity and surface gravity, satisfying a dynamical version
of the so-called first law of black-hole mechanics. A corresponding zeroth law
holds for null trapping horizons, resolving an ambiguity in taking the null
limit.
