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 mass1.0 kg and radius 7.80 cm which operates at 750rev/min. When the power is shut off, you time the grindstone andfind it takes 36.0 s for it to stoprotating. (a) What is the angular acceleration of thegrindstone? (Assume constant angular acceleration.)
1 rad/s2

(b) What is the frictional torque exerted on the grindstone?
2N·m (a) What is the angular acceleration of thegrindstone? (Assume constant angular acceleration.)
1 rad/s2

(b) What is the frictional torque exerted on the grindstone?
2N·m

Explanation / Answer

Initial rotational speed w = 750 rev / min                                        =750 * 2 rad / 60 s                                       = 78.53 rad / s time t= 36 s final angular speed   w ' = 0 Angular accleration = ( w ' - w ) / t                                 = 2.18166 rad / s ^ 2 (b). mass m = 1 kg radius r = 7.8 cm = 0.078 m moment of inertia I = ( 1/ 2) mr ^ 2                             = 0.003042 kg m ^ 2 So, frictional torque T = I                                  =0.0066366 N m

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