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Two rigid plastic panels lie in the planes z = -b and z = b respectively. A rigid ball of radius b can move in the space between the panels and is gripped by them so that it does not slip. The panels are made to rotate with angular velocities ω1k, ω2k about fixed vertical axes that are a distance 2c apart. Show that, with a suitable choice of origin, the position vector R of the centre of the ball satisfies the equationR· = π X R.
where = ½ (ω1 + ω2). Deduce that the ball must move in a circle and find the position of the centre of this circle.
[This arrangement is sometimes seen as a shop window display. The panels are transparent and the ball seems to be executing a circle in mid-air.]
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