  A Kibble balance measures the $gravitational$ mass (weight) of a test mass
with extreme precision by balancing the gravitational pull on the test mass
against the electromagnetic lift force. The uncertainty in such mass
measurement is currently ~$1\times 10^{-8} $. We show how the same Kibble
balance can be used to measure the $inertial$ mass of a test mass, that too
with potentially 50% better measurement uncertainty, i.e., ~$5\times 10^{-9} $.
For measuring the inertial mass, the weight of the test mass and the assembly
holding it is precisely balanced by a counterweight. The application of the
known electromagnetic force accelerates the test mass. Measuring the velocity
after a controlled elapsed time provides the acceleration and, consequently,
the inertial mass of the accelerated assembly comprising the Kibble balance
coil and the mass holding pan. Repeating the measurement with the test mass
added to the assembly and taking the difference between the two measurements
yields the inertial mass of the test mass. Thus, the extreme precision inertial
and gravitational mass measurement of a test mass with a Kibble balance could
provide a test of the equivalence principle. We discuss how the two masses are
related to the Planck constant and other coupling constants and if the Kibble
balance could be used to test the dynamic constants theories in Dirac
cosmology.
