Rolling Motion of a Ball Spinning About a Near-Vertical Axis

Abstract

A ball that is projected forward without spin on a horizontal surface will slide for a short distance before it starts rolling. Sliding friction acts to decrease the translation speed v and it acts to increase the rotation speed ω. When v = Rω, where R is the ball radius, the ball will start rolling and the friction force drops almost to zero since the contact point at the bottom of the ball comes to rest on the surface. The coefficient of rolling friction is much smaller than that for sliding friction. A different situation arises if the ball is projected forward while it is spinning about a vertical or near vertical axis. The latter situation arises in many ball sports. It arises if a player attempts to curve a ball down a bowling alley,1 or when a billiards player imparts sidespin or “English” to a ball,2 and it can arise in golf if a player strikes a ball with a putter at a point well away from the middle of the putter head. The situation also arises in the game of curling,3 although in that case the object that is projected is a cylindrical rock rather than a spherical ball, and it arises in tennis when a ball lands on the court spinning about a near vertical axis, as it does in both a slice serve and a kick serve. In a slice serve, the axis is almost vertical. In a kick serve, the axis is tilted about 30 degrees away from the vertical in order to increase the amount of topspin.4