Particle sliding on a turntable in the presence of friction

Abstract

The motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts a frictional force on the particle that is of constant magnitude and directed opposite to the particle's motion relative to the turntable. After expressing the equations in terms of dimensionless variables, some of the general properties of the solutions are discussed. Approximate analytic solutions are found for the cases in which (i) the particle is released from rest with respect to the lab frame, and (ii) the particle is released from rest with respect to the turntable. The equations are then solved numerically to get a more complete understanding of the motion. It is found that one can define an escape speed for the particle, which is the minimum speed required to get the particle to move out to infinity. The escape speed is a function of both the distance from the center of the turntable and the direction of the initial velocity. A qualitative explanation of this behavior is given in terms of fictitious forces. Numerical study also indicates an alternative way to measure the coefficient of friction between the particle and the turntable.