A pencil can be modeled as a hexagonal prism (in this case). When a pencil rolls on a rough floor, it will rotate around one of its edge, and then the next edge will hit the floor, and then the pencil will continue rotating with the edge as a new rotation axis. To simplify the problem, assume mass of the pencil is concentrated at its center.
Calculate the minimum value of coefficient of friction between the pencil and the floor so that the pencil doesn't slip when its edge hits the floor!
Assume the contact between the pencil and floor only occurs at the pencil's edge.
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