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A uniform disc of radius 0.4 m is free to rotate without friction in a vertical plane about a horizontal axis through its centre. The moment of inertia of the disc about the axis is \(0.2 \mathrm {~kg} \mathrm {~m} ^ { 2 }\). One end of a light inextensible string is attached to a point on the rim of the disc and the string is wound round the rim. The other end of the string is attached to a particle of mass 1.5 kg which hangs freely (see diagram). The system is released from rest. Find
- the angular acceleration of the disc,
- the speed of the particle when the disc has turned through an angle of \(\frac { 1 } { 6 } \pi\).