Rolling Without Slipping — Velocity Profile CM Contact: v=0 Top: v=2v_cm → v_cm ω v_cm = ωR Rolling constraint KE = ½$mv^{2}$(1+$K^{2}$/$R^{2}$) Trans + Rot energy

Key points:

• Contact point: $v = 0$ (rolling constraint)
• CM: $v = v_{cm}$ forward
• Top: $v = 2v_{cm}$ forward
• The rolling body can be treated as rotating about the contact point instantaneously