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 1.4 kg and radius 8.10 cm which operates at 730 rev/min. When the power is shut off, you time the grindstone and find it takes 28.0 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?

Explanation / Answer

a. moment of inertia of grindstone = I
time taken to stop = 28s
let angular deceleration due to friction be a

w = at
w = 730 rev/min = 730*2pi rad / 60 sec = 76.4 rad/s
a = 2.72 rad/s/s

b. frictional torque = aI
I = 0.5mr^2 = 0.7*(0.081)^2 = 0.004
frictional torque = 0.0124 Nm

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