A firm wants to determine the amount of frictional torque in their current line

Question

A firm wants to determine the amount of frictional torque in their current line of grindstones, so they can redesign them to be more energy efficient. To do this, they ask you to test the best-selling model, which is basically a diskshaped grindstone of mass 1.9 kg and radius 9.20 cm which operates at 750 rev/min. When the power is shut off, you time the grindstone and find it takes 36.0 s for it to stop rotating.

(a) What is the angular acceleration of the grindstone? (Assume constant angular acceleration.)

rad/s2

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

N·m

Explanation / Answer

(A) initial angular velocity, wi = 750 rev/min

= 750x 2pi rad/ 60 s

= 78.5 rad/s

wf = 0 (as it stops)

t = 36 s

Applying wf = wi + alpha t

0 = 78.5 + 36alpha

alpha = 2.18 rad/s^2

(B) I = m r^2 /2

and torque = I alpha

= (1.9 x 0.092^2 /2 ) (2.18)

= 0.0175 N m

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