3. A cyclist is riding around a flat, circular track at a constant speed. a) If the radius of the track is r metres and the cyclist is travelling at a speed of w m/s, find their speed and a function that describes the position of the cyclist. Your frame of reference should have the centre of the circle as the origin, the initial point lying on the positive x-axis, and positive orientation. b) Find the normal acceleration (in the case of circular motion, this is also called the centripetal acceleration) of the cyclist. c) Let m kg be the mass of the cyclist and bicycle. Find the force exerted by the track against this mass. d) The resultant of the two vectors above gives the angle at which the cyclist needs to lean in order to avoid tipping over. What is that angle?