  We use the principles of cavity optomechanics to design a resonant mechanical
force sensor for atomic force microscopy. The sensor is based on a type of
electromechanical coupling, dual to traditional capacitive coupling, whereby
the motion of a cantilever induces surface strain that causes a change in the
kinetic inductance of a superconducting nanowire. The cavity is realized by a
compact microwave-plasma mode with an equivalent $LC$ circuit involving the
kinetic inductance of the nanowire. The device is fully coplanar and we show
how to transform the cavity impedance for optimal coupling to the transmission
line and the following amplifier. For the device presented here, we estimate
the bare kinetic inductive mechano-electric coupling (KIMEC) rate $g_0 / 2 \pi$
in the range 3-10 Hz. We demonstrate phase-sensitive detection of cantilever
motion using a multifrequency pumping and measurement scheme.
