Video narration
Why does a fast bicycle turn feel as if it is throwing you outward? In a corner, your motion changes inward: acceleration is a = v2/r. There is no extra centripetal force; that phrase names the inward net force. Analyse the cyclist and bicycle together. Your force diagram has three main forces. On a level road, weight mg pulls downward, normal force N pushes upward, and static friction f at the tires points inward. Vertically, forces balance, so N = mg; friction supplies the inward force, f = mv2/r. The crucial turn: the lean is not merely a steering habit. It lines up the road's combined push with your centre of mass, so it does not twist you over. Balancing torques gives tan(theta) = f/N = v2/(rg), with theta measured from vertical. So higher speed, or a smaller turn radius, demands a larger lean. Why does the corner feel outward? Inertia resists turning; leaning inward aligns the ground's push through your centre of mass, preventing a topple.