Final answer:
The centripetal force keeping a motorcyclist in motion inside a spherical cage in a stunt known as the 'globe of death' is friction between the motorcycle's tires and the cage walls.
Step-by-step explanation:
In the context of a motorcyclist riding inside a spherical cage, the centripetal force that keeps them in uniform circular motion is provided by friction. While gravity does play a role in the system, it does not act toward the center of the path of circular motion. The friction force acts between the tires of the motorcycle and the walls of the spherical cage, pushing toward the center. This force must be constantly present for the motorcyclist to maintain circular motion. Without sufficient friction, the motorcyclist would not be able to continue along the curved path and would be at risk of falling from the cage.