A motor cycle and its rider together have a mass of \(180 \mathrm{~kg}\) and their combined centre of gravity is \(0.6 \mathrm{~m}\) above the ground level when the motor cycle is upright. Each road wheel is of \(0.60 \mathrm{~m}\) diameter and has a moment of inertia \(0.16 \mathrm{~kg} \cdot \mathrm{m}^{2}\). The engine rotates at 5.5 times the speed of the road wheels and in the same sense. Determine the angle of heel necessary when the motor cycle is rounding a curve of \(30 \mathrm{~m}\) radius at a speed of \(50 \mathrm{~km} / \mathrm{h}\).