Frictional Force on a Rolling Disk

A disk of radius R and mass M begins to roll without slipping down a ramp
which makes an angle θ to the horizontal.  Find (a) the value of the frictional
force exerted on the disk by the ramp.  (b) If the angle θ is increased, even
slightly, the disk slips as it rolls.  What is the value of the static coefficient of
friction, μ_s, between the ramp and the disk?  (c) At what angle θ_H will a hoop, having the same coefficient of friction in its interaction with the ramp as the disk, begin to slip?

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