Nature of motion of a bicycle wheel during rolling without slipping: Considering a bicycle moving forward on a road with no skidding, how is the motion of the wheel best described from a rigid-body kinematics perspective?

Introduction / Context:
Rolling motion occurs widely in vehicles and machinery. Understanding that a rolling wheel exhibits both translation of its centre and rotation about its axle is fundamental for analyzing contact kinematics, friction forces, and energy distribution.

Given Data / Assumptions:

• Wheel rolls without slipping on a horizontal surface.
• Deformations are neglected; rigid-body model.
• No external constraints beyond ground contact.

Concept / Approach:

Rolling without slip combines translation of the wheel’s centre of mass with rotation about the axle. The instantaneous centre of rotation lies at the point of contact with the ground where the velocity is momentarily zero, but overall the body experiences both rotational and translational motion simultaneously.

Step-by-Step Solution:

Verification / Alternative check:

Energy-wise, total kinetic energy = translational (1/2 m v^2) + rotational (1/2 I ω^2), confirming both modes are present.

Why Other Options Are Wrong:

(a) ignores rotation; (b) ignores translation of the wheel centre; (d) implies rotation about a fixed external centre (not true except instantaneously at contact); (e) is incompatible with circular point paths (cycloids) on the rim.

Common Pitfalls:

Thinking the bottom point “sticks” and thus the motion is purely rotational; forgetting v = ωR in no-slip rolling.

Final Answer:

rotary and translatory