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.

How long does a rotating square plate take to stop?

00:36 Hint given | 02:28 Solution starts | 06:47 Answer

Question R2L2: Concepts used in solution

Moment of inertia | Dimension analysis | Torque | Angular impulse

Problem statement

A uniform square plate is placed on a rough horizontal floor hinged at one corner. When it is given an angular velocity w about a vertical axis through this corner, as shown in figure(a), it takes time t to come to a complete stop. Now the same square plate is hinged about the center and given the same angular velocity about a vertical axis as shown in figure(b). How long will it take to come to a complete stop now?