This work analyzes the energy harvested by a piezoelectric vibration energy harvester that is attached to a rotating host system, like an automotive tire, that has superposed translational vibration. The device experiences once-per-revolution dynamic excitation from rotation and, because the host system translates, additional speed-dependent excitation from input vibration. The device consists of a piezoelectric beam with a proof mass that displaces tangentially in operation so that large, troublesome centripetal accelerations can be avoided. The dynamic response and power harvested are determined in closed-form. The speed-dependent properties of the response components are determined. With excitation from rotation and vibration, the device harvests substantially more power than if the system were excited by either rotation or vibration alone. Numerical results are shown for an example device over a wide range of rotation speeds. The device can harvest 185 mW of power at its maximum when the rotation speed is near 1,000 rpm. The device provides more than 30 mW of power for speeds between 817 rpm and 1,195 rpm. Harvesting energy from vibration naturally leads to wider speed bandwidths where large amounts of power are available.