Question

Consider a uniform disk of radius R and mass m sliding down an incline making an angle θ with respect to the horizontal. The coefficient of kinetic friction between the disk and the surface is μk. The torque due to friction causes the disk to rotate as it slides down the incline.

a) Compute the linear acceleration of the disk as it slides down the incline.

b) Compute the angular acceleration of the disk as it slides down the incline.

c) Is it possible for the disk to spin more rapidly while sliding than if it were rolling without slipping? If so, under what conditions?

Answer 1

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Sliding as IN mgsino How N = Mg cos - Mgcolso So, frictional force fx = Men - fx = Mx Mgcoso a) acceleration of dice et Mą= Mg sino - FK S Mą= Mg sino - Mx Mg coso - as = g sino - Megcoso b) Moment of iner ha of clisc I - MRS Torque = I do Fox R = MR² HA Mg coso x R = MR² as As = ?uk g coso R c) Angular accelera hon of disc while rolling 6. de Roi <, > <eы. Byun acoso seguiment of Histoire