What is the acceleration of these pure rolling rings?

00:46 Hint given | 01:51 Constraint equation | 04:32 Force solution | 08:51 Energy solution | 11:28 Answer

Question GM3L3: Concepts used in solution

F=ma | Constraint equation | Energy conservation | Torque

Problem statement

Two identical rings of mass M and radius R stand on a rough horizontal surface. The rings are in contact at point P. The radius vector to P makes an angle theta with the horizontal as shown in the figure.  A small cylindrical object of mass m is placed symmetrically on the rings at point P and released. It slides on the rings without friction. Find the acceleration of the center of the rings immediately after the release. The rings do not slip on the surface.