Hold a pen (or pencil, ruler etc.) using your two index fingers with your fingers at the ends of the object. Now move your two fingers toward each other. Assuming the frictional force provided by both fingers is identical, they should meet at the center of mass of the object, with your fingers alternating between being stationary and moving. When going backwards from the centre, one finger stays stationary the whole time. Why is this the case?
I have a general 'hand-wavey' explanation (the closer to the centre of mass a finger is, the greater the reaction force and thus the frictional force exerted, the finger with less friction moves until it is holding more weight and the frictional force becomes too large...) but I am looking for a much better detailed (mathematical if necessary) explanation including all the forces at play, torque, moments etc.
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