= Initial acceleration of three stacked cylinders
{title2=$a_{\mathrm{top}}=g/(7+6\beta)\ \mathrm{or}\ g/(7+8\beta)$}
Three identical cylinders initially form an equilateral triangle on a horizontal floor and are released from rest. If each has <moment of inertia> $\beta mR^2$, the initial top downward <acceleration> is $g/(7+6\beta)$ for no-slip rough ground and smooth cylinder contacts, or $g/(7+8\beta)$ for smooth ground and no-slip rough cylinder contacts. In both cases the lower cylinders separate with outward <acceleration> $u=\sqrt3a_{\mathrm{top}}$. The corresponding lower-cylinder <angular acceleration> magnitudes are $u/R$ and $2a_{\mathrm{top}}/R$, with opposite rotation senses between the cases. Sufficient <static friction> is required; a finite coefficient allowing sliding changes the problem.
Back to article page
