Each wheel of a motorcycle is of 600 mm diameter and has a moment of inertia of 1.2 kg.m2 . The total mass of the motorcycle and the rider is 180 kg and the combined mass is 580 mm above the ground level when the motor cycle is upright. The moment of inertia of the rotating parts of the engine is 0.2 kg.m2 . The engine speed is 5 times the speed of the wheels and is in the same sense. Determine the angle of heel necessary when the motor cycle takes a turn of 35 m radius at a speed of 54 km/h.