What physical law explains why matter flowing from the companion star orbits rapidly as nears the black hole?

Newtons equations the motions of objects in orbit. The force of gravity acting on a an object is described by the equation:
#F=(GMm)/r^2#
Where #G# is the gravitational constant, #M# is the mass of the body the object is orbiting around, #m# is the mass of the orbiting object and #r# is the distance apart.

The centripetal force required to keep an object in orbit is given by the equation:
#F=(mv^2)/r#
Where #v# is the speed of the orbiting object.

When an object is in orbit these two forces are equal:
#(GMm)/r^2=(mv^2)/r#
Dividing by #m# and multiplying by #r# gives:
#v^2=(GM)/r#

In the scenario #M# is the mass of the black hole which will be quite large. The black hole will also be quite small. As the matter gets closer to the black hole the value of #r# will get progressively smaller and hence the speed #v# will get progressively larger.

Hence the closer matter is to the black hole the faster it will orbit.

Once matter gets quite close to a black hole the effects of general relativity become significant, but Newtons equations of motion are close enough at greater distances.