Rolling without slipping
The kinematic constraint v = ω·R that locks a wheel's linear velocity to its rotation so the contact point is momentarily at rest.
Definition
When a wheel, ball, or cylinder rolls along a surface without its contact patch sliding, the instantaneous velocity of the point touching the ground is zero. The rest of the body moves as a combination of translation of the centre of mass at v_CM and rotation about that centre at angular velocity ω. Locking those motions together gives the constraint v_CM = ω·R, where R is the radius. Differentiating in time yields a_CM = α·R, linking linear and angular acceleration.
The constraint couples Newton's second law for translation to its rotational counterpart τ = I·α, producing a_CM = F / (m + I/R²) for a body pushed at its axle. Because I depends on how mass is distributed, shapes with mass concentrated at their rim (hoops, hollow cylinders) accelerate more slowly than shapes with mass near the axis (solid cylinders, spheres). This is why a solid ball beats a hollow one down a ramp of equal mass and radius.