An Exploded Disc

Extract

The problem of a disc supported on two pegs and disturbed by a horizontal force has been recently discussed by Griffin, Skelsey and Scorer (1965) mainly in terms of limiting equilibrium. However the way in which limiting equilibrium is approached, and breaks down through a transitional slipping at one peg, can be discussed within the simple laws of friction, provided only that we assume the peg supports are not perfectly rigid and obey some law of elasticity in providing a reaction opposite to their displacement. In the case when the pegs are far enough apart for the disc to be jammed between them, the reactions at the pegs may be indefinitely large, limited only by the breaking strength of the pegs or the possibility that the pegs may be forced so far apart as to allow the disc to pass between them. If the horizontal force on the disc is increased, equilibrium is then broken by slipping at one of the pegs, which is unrestrained and explosive. The cases of small and large friction coefficient are indistinguishable as limiting equilibrium states, because the disc is performing accelerated rotation about the other peg when either the pressure on the first peg becomes zero or slipping starts at the second peg. Thus in the case θ>λ>90θ – 2θ considered by Miss Griffin the limiting equilibrium state considered is not always attainable. Also the case quoted by Miss Skelsey under diagram 15 wherein equilibrium is never broken is physically impossible unless one of the pegs has a negative elastic constant or some additional mechanism is provided to increase the pressure between the pegs as the disturbing force is increased.