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?