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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 1.3 kg and radius 8.50 cm which operates at 700 rev/min. When the power is shut off, you time the grindstone and find it takes 41.3 s for it to stop rotating.

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Answer:

0.00833542627085 Nm

Explanation:

[tex]\omega_f[/tex] = Final angular velocity = 700 rpm

[tex]\omega_i[/tex] = Initial angular velocity

[tex]\alpha[/tex] = Angular acceleration

m = Mass of stone = 1.3 kg

r = Radius = 8.5 cm

[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\dfrac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\dfrac{0-700\dfrac{2\pi}{60}}{41.3}\\\Rightarrow \alpha=-1.77491110372\ rad/s^2[/tex]

Torque is given by

[tex]\tau=-I\alpha\\\Rightarrow \tau=-\dfrac{1}{2}mr^2\alpha\\\Rightarrow \tau=-\dfrac{1}{2}1.3\times 0.085^2\times -1.77491110372\\\Rightarrow \tau=0.00833542627085\ Nm[/tex]

The frictional torque is 0.00833542627085 Nm

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