  Nuclear spins in certain solids couple weakly to their environment, making
them attractive candidates for quantum information processing and inertial
sensing. When coupled to the spin of an optically-active electron, nuclear
spins can be rapidly polarized, controlled and read via lasers and
radiofrequency fields. Possessing coherence times of several milliseconds at
room temperature, nuclear spins hosted by a nitrogen-vacancy center in diamond
are thus intriguing systems to observe how classical physical rotation at
quantum timescales affects a quantum system. Unlocking this potential is
hampered by precise and inflexible constraints on magnetic field strength and
alignment in order to optically induce nuclear polarization, which restricts
the scope for further study and applications. In this work, we demonstrate
optical nuclear spin polarization and rapid quantum control of nuclear spins in
a diamond physically rotating at $1\,$kHz, faster than the nuclear spin
coherence time. Free from the need to maintain strict field alignment, we are
able to measure and control nuclear spins in hitherto inaccessible regimes,
such as in the presence of a large, time-varying magnetic field that makes an
angle of more than $100^\circ$ to the nitrogen-lattice vacancy axis. The field
induces spin mixing between the electron and nuclear states of the qubits,
decoupling them from oscillating rf fields. We are able to demonstrate that
coherent spin state control is possible at any point of the rotation, and even
for up to six rotation periods. We combine continuous dynamical decoupling with
quantum feedforward control to eliminate decoherence induced by imperfect
mechanical rotation. Our work liberates a previously inaccessible degree of
freedom of the NV nuclear spin, unlocking new approaches to quantum control and
rotation sensing.
