= Energy-preserving change of rolling radius
{title2=$v_f/v_i=\sqrt{(m+I/h_i^2)/(m+I/h_f^2)}$}
A <rigid body> rolling with effective <radius> $h$ has <kinetic energy> $(m+I/h^2)v^2/2$. If a transition changes the rolling constraint while preserving this total <energy>, the translational <speed> changes according to the title formula. Maintaining the same <speed> would generally require <energy> loss or gain. The energy-preserving condition is an assumption about the transition, not a generic property of sudden impacts.
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