In this paper we present theoretical model calculations involving Monte Carlo computer simulations of Compton scattering and electron-positron (e-e+) pair production processes in the ergosphere of a supermassive rotating black hole. Particles from an accretion disk surrounding the rotating black hole fall into the ergosphere and are scattered by particles that are confined in equatorial and nonequatorial orbits. The energy-momentum vectors are calculated for the scattered escaping particles. Particles escape with energies of about 3 GeV or greater. Importantly, these model calculations show that the Lense-Thirring effect, that is, the dragging of local inertial frames into rotation, inside the ergosphere, caused by the angular momentum of the rotating black hole, results in a gravitomagnetic force being exerted on the scattered escaping particles. Effects of this force on the Penrose scattered particles are analyzed and discussed.