We recently used a new ferrite rf dipole to study spin flipping of a 2.1 GeV/c vertically polarized proton beam stored in the COSY Cooler Synchrotron in Jülich, Germany. We swept the rf dipole's frequency through an rf-induced spin resonance to flip the beam's polarization direction. After determining the resonance's frequency, we varied the frequency range, frequency ramp time, and number of flips. At the rf dipole's maximum strength and optimum frequency range and ramp time, we measured a spin-flip efficiency of 99.92+/-0.04%. This result, along with a similar 0.49 GeV/c IUCF result, indicates that, due to the Lorentz invariance of an rf dipole's transverse integralBdl and the weak energy dependence of its spin-resonance strength, an only 35% stronger rf dipole should allow efficient spin flipping in the 100 GeV BNL RHIC Collider or even the 7 TeV CERN Large Hadron Collider.