  We study the thermodynamics of $AdS_4$ black hole solutions of
Einstein-Maxwell theory that are accelerating, rotating, and carry electric and
magnetic charges. We focus on the class for which the black hole horizon is a
spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions
of $D=11$ supergravity that are free from conical singularities. We use
holography to calculate the Euclidean on-shell action and to define a set of
conserved charges which give rise to a first law. We identify a complex locus
of supersymmetric and non-extremal solutions, defined through an analytic
continuation of the parameters, upon which we obtain a simple expression for
the on-shell action. A Legendre transform of this action combined with a
reality constraint then leads to the Bekenstein-Hawking entropy for the class
of supersymmetric and extremal black holes.
