Rolling Motion

Rolling without slipping: a rotating body translates AND rotates, with v_CM = R·ω (rolling condition).

The point of contact with the ground is INSTANTANEOUSLY AT REST.

Total KE of a rolling body: K = ½Mv² + ½Iω². For rolling condition: K = ½Mv²(1 + I/MR²).

Rolling friction acts at contact point — small (compared to sliding friction) because the contact area doesn't slip.

Static friction at contact provides the torque for rolling — it does NO WORK (point of contact at rest).

On an incline: a = g·sin θ / (1 + I/MR²). Different bodies have different accelerations.

Solid sphere rolls fastest on an incline, hollow ball slower, then ring slowest — depends on I/MR² ratio.

Pure rolling: no energy lost to friction. Slipping: kinetic friction acts and energy is lost.