= Reflected inertia of a no-slip wheel and roller
{title2=$K=I+J(R/S)^2$}
If a fixed-axis wheel of radius $R$ drives a fixed-axis roller of radius $S$ without slip, their angular-speed magnitudes satisfy $\sigma=(R/S)\omega$. Their <kinetic energy> is $\tfrac12[I+J(R/S)^2]\omega^2$, so the displayed reflected <moment of inertia> governs the wheel coordinate. A roller resisting torque of magnitude $\gamma\sigma^2$ consumes power $\gamma\sigma^3$ and therefore reflects to wheel torque $\gamma(R/S)^3\omega^2$. The squared ratio belongs to inertia; the cubed ratio belongs to this quadratic resisting torque.
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