Vehicle Dynamics — Leaning While Negotiating a Curve When a person rides a bicycle around a curve at speed, to maintain equilibrium they must lean in which direction relative to the curve?

Introduction / Context:
Cornering on a bicycle or motorcycle requires balancing lateral (centripetal) acceleration with gravitational force. The rider adjusts their lean angle to align the resultant of these forces through the combined center of mass to avoid tipping.

Given Data / Assumptions:

• Steady turn at speed v on a curve of radius R.
• Neglect transient steering inputs and road camber for the core concept.

Concept / Approach:
The required centripetal force is m v^2 / R toward the center. Gravity acts downward with mg. The rider leans inward so the resultant of mg and m v^2 / R passes through the tire contact patch, maintaining no net tipping moment about the contact point.

Step-by-Step Solution (qualitative):

Verification / Alternative check:
As speed increases or radius decreases, tan θ increases; riders visibly lean more at higher speeds or tighter turns, confirming inward lean.

Why Other Options Are Wrong:
Leaning outward would shift the resultant outside the base of support and cause overturning; standing upright is only feasible at infinitesimal speeds (v ≈ 0).

Common Pitfalls:
Confusing the direction of friction with the direction of the required lean; assuming banking of the road eliminates the need to lean—it only reduces the required lean angle.

Final Answer:
Inward (toward the center of curvature).