  While supermassive black hole masses have been cataloged across cosmic time,
only a few dozen of them have robust spin measurements. By extending and
improving the existing Event Horizon Telescope (EHT) array, the next-generation
Event Horizon Telescope (ngEHT) will enable multifrequency, polarimetric movies
on event horizon scales, which will place new constraints on the space-time and
accretion flow. By combining this information, it is anticipated that the ngEHT
may be able to measure tens of supermassive black hole masses and spins. In
this white paper, we discuss existing spin measurements and many proposed
techniques with which the ngEHT could potentially measure spins of target
supermassive black holes. Spins measured by the ngEHT would represent a
completely new sample of sources that, unlike pre-existing samples, would not
be biased towards objects with high accretion rates. Such a sample would
provide new insights into the accretion, feedback, and cosmic assembly of
supermassive black holes.

High Energy Astrophysical Phenomena