This simulation shows the motion of a ball rolling without slipping in a cone under the influence of gravity and friction. The ball can be started out at a position (x, y) relative to an origin at the center of the cone, with an initial velocity (v_x, v_y ).

The Rolling Friction parameter determines how fast the ball slows down when rolling on a flat surface. The time for the ball to slow down by one revolution per second when rolling on a flat surface is displayed as the Rolling Decay Time. The Spinning Friction parameter determines how fast the ball slows down when spinning on a flat surface. The time to slow down by one revolution per second when spinning on its axis is displayed as the Spin Decay Time. The rolling and spinning friction need not be closely related. This is a property of the ball. These parameters can be adjusted to attain a realistic motion.

You may choose either a solid ball or a hollow one, or something with a different internal mass density, if desired. The mass distribution in the ball determines how fast it accelerates. A solid ball will accelerate faster than an otherwise identical hollow one because it has a lower moment of inertia. The Ball Inertia is a coefficient proportional to the moment of inertia, and is determined by how the mass is distributed in the ball. It is 2/5 for a solid ball. The upper limit is 2/3, for a sphere with all its mass on the surface. This parameter would be 0if all the mass were concentrated at the center of the ball.

The energy, and orbit and spin angular momenta are conserved in the absence of rolling or spinning friction. The orbital angular momentum is the angular momentum for the ball center of mass motion relative to the vertical axis through the center of the cone. The spin angular momentum is the angular momentum of the spinning ball about a vertical axis through its center.

The speed at which the ball is spinning about an axis perpendicular to the cone is determined by the spin angular momentum and distance from the center. The spinning speed is indicated by the color of the ball: purple for no spin, red for maximal spin, and green for intermediate speeds.

Scott A. Yost, 2000.