This question describes a simplified model of a device used to de-spin a satellite.

This question describes a simplified model of a device used to de-spin a satellite. A uniform circular disc of mass 12m and radius a lies on a smooth horizontal table and is free to rotate about a fixed vertical axis through its centre. A light wire is attached to a point on the rim of the disc and is wound round this rim. A particle of mass m is attached to the free end of the wire and is initially attached to the rim. When the disc is rotating with angular speed in the opposite sense to that in which the wire is wound the particle is released so that the wire unwinds and remains taut. The length of the wire is chosen so that it is completely unwound at the instant that the disc stops rotating. The particle is then moving at right angles to the wire. Use the principles of conservation of angular momentum and energy to find the length of the wire.