Question

Three small balls of the same mass, white (w), green (g), and blue (b), are fixed by weightless rods at the vertices of the equilateral triangle with side l. The system of balls is placed on a smooth horizontal surface and set in rotation about the centre of mass with period T. At a certain instant, the blue ball tears away from the frame.

Determine the distance L between the blue and the green ball after the time T.

Answer 1

During the time T, the distance covered by the blue ball is

(Fig. 174), where ω = 2pi/T is the rotational frequency. During the same time, the centre of mass of the green

and the white ball will be displaced by a distance

The rod connecting the green and the white ball will simultaneously turn through an angle 2pi since the period of revolution of the balls around their centre of mass coincides with the period T. Therefore, the required distance is

or for another arrangement of the balls (the white and the green ball change places in the figure),