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 disk shaped grindstone of mass 1.1 kg and radius 7.70 cm which operates at 750 rev/min. When the power is shut off, you time the grindstone and find it takes 38.0 s for it to stop rotating. (a) What is the angular acceleration of the grindstone? (Assume constant angular acceleration.) rad/s^2 (b) What is the frictional torque exerted on the grindstone? N.m A 2.3-kg 13-cm-radius cylinder, initially at rest, is free to rotate about the axis of the cylinder. A rope of negligible mass is wrapped around it and pulled with a force of 18 N. (a) Find the magnitude of the torque exerted by the rope. N middot m (b) Find the angular acceleration of the cylinder. rad/s^2 (c) Find the angular velocity of the cylinder at t = 1.20 s. rad/s

Explanation / Answer

1) = /t = -750rev/min * 2 rad/rev * 1min/60s / 38.0s = -2.067 rad/s²
= I = ½ * 1.1kg * (0.077m)² * 2.067rad/s² = 0.0067 N·m

2) (a) torque = T * r = 18N * 0.13m = 2.34 N·m

(b) I = ½mr² = ½ * 2.3kg * (0.13m)² = 0.0194 kg·m²
= / I = 2.34N·m / 0.0194kg·m² = 120.6 rad/s²

(c) = *t = 120.6rad/s² * 1.2s = 144.7 rad/s

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