Induced Rocking

Abstract

Circular objects such as disks fitted with central spindles rest on a horizontal table in inclined positions which are in neutral equilibrium. If the disk is loaded eccentrically with a small body the disk will rest in stable equilibrium when that body is in its lowest position. If the whole is displaced to one side and released it will rock to and fro about that position. Theory and experiment are applied to find how the period of the rocking motion depends on the dimensions of the disk, spindle, and affixed body, the inclination of the spindle to the horizontal, and the masses and moments of inertia of disk, spindle, and affixed body. The expression found for the length L of the equivalent simple pendulum is L = I cosρ/ma, where I is the total moment of inertia of disk, spindle, and affixed body about the line joining the points of contact of the spindle and the disk with the table, ρ is the angle of inclination of the spindle to the horizontal, m is the mass of small affixed body, and a is the distance of the center of this body from the axis of the disk and spindle.