Transition from bouncing to rolling on a horizontal surface.

If a ball is incident obliquely on a horizontal surface and is allowed to bounce more than once, then it is likely to bounce many times before it starts rolling along the surface. The number of bounces before rolling commences depends on the initial vertical speed and the normal coefficient of restitution. The transition from bouncing to rolling is examined using a simple theoretical model and is compared with experimental data obtained by filming the process with a video camera. We find that the final rolling speed is proportional to the initial horizontal speed of the ball and depends on the initial ball spin, but is independent of the tangential coefficient of restitution. Representative videos for different balls are included as supplementary material, including a superball thrown with a backspin that creates a back and forth motion. Instructors could use the experiment and/or analysis for an advanced undergraduate lab or use a simplified observational exercise for non-majors. Editor's Note: When a ball is dropped on a horizontal surface with no initial spin, previous studies have found that its bouncing behavior can be simply described using a coefficient of restitution, which gives the ratio of the velocity after the bounce to before the bounce. The value of this coefficient is −1 for a perfectly elastic ball/surface, with a smaller magnitude for any real ball. In many sports, like golf, basketball, or bowling, balls are thrown at an angle and are often given some initial spin by the player. Depending on initial conditions, these balls can bounce, roll, or start by bouncing and then transition to rolling. Here, the transition from bouncing to rolling is shown to be described by using both a vertical and horizontal coefficient of restitution, with the horizontal velocity defined at the spinning edge of the ball rather than its center. Videos of undergraduate level experiments are included, with results used to validate the model. [ABSTRACT FROM AUTHOR]