Black hole mechanics was recently extended by replacing the more commonly u
sed event horizons in stationary space-times with isolated horizons in more
general space-times (which may admit radiation arbitrarily close to black
holes). However, so far the detailed analysis has been restricted to nonrot
ating black holes (although it incorporated arbitrary distortion. as well a
s electromagnetic, Yang-Mills, and dilatonic charges). We now fill this gap
by first introducing the notion of isolated horizon angular momentum and t
hen extending the first law to the rotating case.