= Effective mass of a rolling rigid body
{title2=$M_{\rm eff}=M+I/r^2$}
For <rolling without slipping> with contact radius $r$, substitute $\omega=v/r$ into translational plus rotational <kinetic energy>:
$$
T=\frac12Mv^2+\frac12I\omega^2=\frac12\left(M+\frac I{r^2}\right)v^2.
$$
The coefficient acts as an effective inertia for a translation coordinate. It is not additional gravitational <mass>. A quadratic <potential energy> $Kx^2/2$ then gives small-oscillation frequency $\omega_0=\sqrt{K/M_{\rm eff}}$ when this coefficient is constant.
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