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I have a question about the center of rotation. If there is a bar which has 60°degree with the horizontal surface and one end is touching the surface. The bar start to fall at rest. Bar is rigid body and surface has friction. So the bottom end won't move.

In this situation bar rotates about the bottom end. But if the bottom end begin to slip then the bar rotates about the center of mass of the bar? Or do I have to think that bar still rotates about the bottom end and the bottom end is moving toward x-axis? If the latter is right. I can think about the moving reference frame. Am I right?

Any help would be appreciated!

Lee
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1 Answers1

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We can actually take rotation about any point but the center of mass frame is useful as then no fictional/pseudo forces have to be considered( they will all give the same result).

Consider this force diagram, taking the center of mass frame. At the instant when the bar is released from rest, taking the center of mass as pivot, if the opposite torques created by friction(F) and normal reaction force(N) are equal then so slipping happens at point on ground( as it has zero net torque on it).

Now if friction is not enough( F is less) than the anti clockwise torque of N will be greater now. So at that instant the rod rotates a tiny bit(moving upwards and outwards in a direction perpendicular to rod) and loses contact with the ground then the only force on it is its weight(mg) which has no torque about center of mass but it brings the end down to the ground again and the process can repeat( this complicated mechanism is the slippage ).

Hope this helps.

Tausif Hossain
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