A uniform horizontal disk of mass M and radius R is rotating about its vertical axis with

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A uniform horizontal disk of mass M and radius R is rotating about its vertical axis with an angular velocity ω. When it is placed on a horizontal surface, the coefficient of kinetic friction between the disk and surface is μk

(a) Find the torque dτ exerted by the force of friction on a circular element of radius r and width dr. 

(b) Find the total torque exerted by friction on the disk. 

(c) Find the time required to bring the disk to a halt.

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