10.1119/1.4914559_1

A routine problem in an introductory physics course considers a rectangular block at rest on a plane inclined at angle α to the horizontal. In order for the block not to slide down the incline, the coefficient of sliding friction, μ, must be at least tan α. The situation is similar for the case of a ball rolling down an inclined plane. In order for a solid ball to roll without slipping down the inclined plane, μ must be at least (2/7) tan α. In both cases, static friction is responsible for the observed effects and one can find treatments of these topics in most introductory physics textbooks. Notice that when α = 0, no frictional force is required for the ball to roll at constant speed, just as no frictional force would be required to keep the rectangular block from sliding on a horizontal plane. In the case of a rolling ball that is accelerating, a frictional force acts to produce a torque about the center of mass and, thus, plays an important role in the acceleration of the ball, whether on a horizontal1,2 or inclined plane.