A solid sphere of radius R and mass M is rolling without slipping on a horizontal surface with a linear speed v. What is the angular momentum of the sphere about a point on the surface?

Core Concept

The angular momentum about a point on the surface is the sum of the angular momentum about the center of mass plus the angular momentum due to the center of mass motion. For a solid sphere, I = (2/5)MR², so L_cm = Iω = (2/5)MR²(v/R) = (2/5)MvR. The angular momentum due to center of mass motion is MvR. Total L = (2/5)MvR + MvR = (7/5)MvR.