Stanton D. answered • 03/03/16

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Chantelle,

You're exactly on the right track; she has to grip it tighter in order to exert a frictional force sufficient to keep the chain from slipping through her fingers. Now, you know that frictional force opposes whatever tendency the chain has to slip: in other words, her fingers are (passively) pulling the chain inwards to provide centripetal force to the chain. Each piece of the chain is following its own circular path; to change the momentum of a mass requires a force; to keep a mass moving in a circle at constant speed requires a centripetal force of constant magnitude, in a direction at right angles to that circular path at that moment.

So -- a = v^2/r = .omega.^2 * r

F(centripetal) = m * a

F(friction) == F(centripetal)

What may be tricky here, is adding up all the pieces of chain, each with its particular circle. That math depends on exactly how the chain is being swung -- in a conical arc, or oriented around a horizontal axis, and so on.

Hope this allows you to start calculating!