A firm wants to determine the amount of frictional torque in theircurrent line o

Question

A firm wants to determine the amount of frictional torque in theircurrent line of grindstones, so they can redesign them to be moreenergy efficient. To do this, they ask you to test the best-sellingmodel, which is basically a diskshaped grindstone of mass 1.3 kgand radius 7.50 cm which operates at 720 rev/min. When the power isshut off, you time the grindstone and find it takes 32.3 s for itto stop rotating.
(a) What is the angular acceleration of the grindstone (inrad/s2)?

(b) What is the frictional torque exerted on the grindstone(N*m)?

Explanation / Answer

mass m = 1.3 kg radius r = 7.5 cm =0.075 m Moment of inertia I = ( 1/ 2) m r ^ 2                              = 0.00365625 kg m^2 Initial angular speed w = 720 rev / min                                   = 720 * 2 rad / 60 s                                   = 75.39 rad / s time t= 32.3 s final angular speed w ' = 0 from the relation w ' = w + t angular accleration = [ w ' - w ] / t                                = - 2.3343 rad / s ^ 2 (b).  magnitude of the frictional torque exerted onthe grindstone = I                                                                                                 = 0.00853 N m

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