Probability, geometry and dynamics in the toss of a thick coin
Probability, geometry and dynamics in the toss of a thick coin.
E-H. Yong, L. Mahadevan, American Journal of Physics 79(12):1195-1201, 2011.
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Abstract
When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic
substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and
precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a
function of its dimensions and the distribution of its initial conditions. Our theory yields a simple
expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads or tails
compared to sides, which we validate using data from the results of tossing coins of different
aspect ratios.