A circular hoop of mass , radius , and infinitesimal thickness rolls without sli

Question

A circular hoop of mass , radius , and infinitesimal thickness rolls without slipping down a ramp inclined at an angle with the horizontal. Part A What is the acceleration of the center of the hoop? Express the acceleration in terms of physical constants and all or some of the quantities m,r ,theta Part B What is the minimum coefficient of (static) friction needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, since the bottom point on the wheel is not moving relative to the ground (this is the meaning of no slipping).

Explanation / Answer

(Express the acceleration in terms of physical constants and all or some of the quantities m, r, and theta.) a=g/2*sin(theta) the same for all matter going down an incline b)What is the minimum coefficient of (static) friction mu_min needed for the hoop to roll without slipping? Note that it is static and not kinetic friction that is relevant here, since the bottom point on the wheel is not moving relative to the ground (this is the meaning of no slipping). (Express the minimum coefficient of friction in terms of all or some of the given quantities m, r, and theta.) mu_min= Fnet = Fg + Fs = 0 = mgsin(theta) + -mgcos(theta)*us us min = tan/2(theta)

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