Winds blown from accretion disks formed inside massive rotating stars may result in stellar explosions observable as Type Ibc and Type II supernovae. A key feature of the winds is their ability to produce the radioactive Nickel-56 necessary to power a supernova light curve. The wind strength depends on accretion disk cooling by neutrino emission and photo-disintegration of bound nuclei. These cooling processes depend on the angular momentum of the stellar progenitor via the virial temperature at the Kepler radius where the disk forms. The production of an observable supernova counterpart to a Gamma-Ray Burst (GRB) may therefore depend on the angular momentum of the stellar progenitor. Stars with low angular momentum may produce a GRB without making an observable supernova. Stars with large angular momentum may make extremely bright and energetic supernovae like SN 1998bw. Stars with an intermediate range of angular momentum may simultaneously produce a supernova and a GRB.