Steps for

Exercise $2$

Attached to a uniformly rotating shaft are four discs, $A,B,C$ and D $,$ spaced at equal

intervals along the shaft, of mass $7,5kg,12,5kg,7kg$ and $6$ kg respectively; the centres of

mass of the discs are at $4mm,3mm,5$mmand$8mm$ respectively from the axis of rotation.

An additional mass $M$ may be attached to $D$ at an effective radius of $60$ mm from the axis of

rotation.

Find the minimum value of the mass of M $,$ and the relative angular positions of the centres of

mass of all the masses to ensure complete dynamic balance for the rotating shaft.