The problem of a body slipping down a frictionless hemisphere is very common in physics and engineering textbooks. In this type of problem, students are normally asked to find the angle at which the body flies off the surface. In this work, we have constructed an apparatus to determine the angle at which a ball flies off a circular track, and to study the motion of the ball (rolling and slipping) along the surface. The apparatus is comprised of two parallel rails that form a quarter circle. The angular position and velocity of a steel ball are measured using a moveable arm equipped with a photodetector. Two methods are used to determine the angle the ball loses contact with the track. Both methods provide values in agreement with a model for rolling followed by slipping.
The Rayleigh's dissipation function is used to derive the expressions of dissipative forces that can not be obtained from a potential energy function. These expressions are then used in the Lagrange's equations in a formulation that accommodates dissipation.