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1 (a) (i) Define the radian. (ii) A small mass is attached to a string. The mass is rotating about a fixed point P at constant speed, as shown in Fig. 1.1. Explain what is meant by the angular speed about point P of the mass. (b) A horizontal flat plate is free to rotate about a vertical axis through its centre, as shown in Fig. 1.2. A small mass M is placed on the plate, a distance d from the axis of rotation. The speed of rotation of the plate is gradually increased from zero until the mass is seen to slide off the plate. The maximum frictional force F between the plate and the mass is given by the expression F = 0.72W, where W is the weight of the mass M. The distance d is 35cm. Determine the maximum number of revolutions of the plate per minute for the mass M to remain on the plate. Explain your working. (c) The plate in (b) is covered, when stationary, with mud. Suggest and explain whether mud near the edge of the plate or near the centre will first leave the plate as the angular speed of the plate is slowly increased.