Comment on ‘Dynamics of a bouncing capsule: An impulse model vs a Hertzian model’

Li et al.¹ provide interesting experimental and theoretical results on the bounce of a capsule dropped vertically onto a horizontal surface. If the capsule is incident with spin, then it can bounce to a slightly greater height than the drop height. There is no net gain in energy since rotational kinetic energy is converted to vertical translational kinetic energy during the bounce. The effect is relatively small when the capsule is incident vertically, but can be much more dramatic if the capsule, or any other elongated object, is incident obliquely with spin on a horizontal surface. Then, translational kinetic energy due to horizontal motion can be converted into translational kinetic energy in the vertical direction. A well-known example is the pole vault. Experiments with a spinning plastic egg² or two golf balls joined together³ show that the vertical coefficient of restitution (COR) can vary from about –4 to about +2 if the COR is defined in terms of the vertical speeds of the center of mass or in terms of the drop and bounce heights. The effect can be observed by eye without the need for accurate measurements and makes for a visually appealing lecture demonstration. Rugby football spectators will be familiar with an oval shape football that bounces along the ground several times then suddenly jumps to about the head height.