Final answer:
Adding a bias to the lean angle ensures the perpendicular forces exerted by the ground align with the bicycle's center of gravity, aiding in balance. It provides the centripetal force necessary for turning and correlates the angle of lean with speed and radius of curvature, essential for stability.
Step-by-step explanation:
The purpose of adding a bias to the lean angle when riding a motorcycle, or in this case a bicycle, is to ensure the rider can maintain balance while turning. Leaning at the correct angle makes certain that the force exerted by the ground is aligned with the center of gravity of the system (cyclist and bicycle), which helps the rider stay upright and avoid tipping over. When a bicycle turns, the force on the tires can be decomposed into two perpendicular components: the friction force (parallel to the road), which provides the centripetal force necessary for the turn, and the normal force (vertical), which counteracts the system's weight.
Moreover, when a cyclist leans at the correct angle, this also establishes a relationship between the angle of lean, the speed of travel (v or u), and the radius of curvature of the turn, which is crucial for maintaining balance and stability due to the physics involved in the motion similar to that observed in the ideal banking of roadways.