In the March 2019 issue, Scott Rubin analyzes the motion of a snowball rolling without slipping down a snowy inclined plane (making angle θ with the horizontal) and accreting additional snow as it does so.1
Equations (12) and (13) of Rubin’s paper are two coupled differential equations for v and r, but they cannot be solved analytically in terms of elementary functions of independent variable t. Instead, Rubin performs a numerical integration in a spreadsheet to find v (t), along with the translational acceleration a(t) of the snowball’s center of mass.
However, it is possible to find v and a analytically as a function of a different independent variable, namely the snowball’s radius r. This result is arguably even more useful than knowing how v and a vary with time, because we can directly relate r to the distance s the snowball...