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 1.1 kg and radius 0.09 m which operates at 73.3 rad/s. When the power is shut off, you time the grindstone and find it takes 42.4 s for it to stop rotating. What is the frictional torque exerted on the grindstone in newton-meters

Answer 1

Explanation:

Mass of the diskshaped grindstone, m = 1.1 kg

Radius of disk, r = 0.09 m

Angular velocity, $\omega=73.3\ rad/s$

Time, t = 42.4 s

We need to find the frictional torque exerted on the grindstone. Torque in the rotational kinematics is given by :

$\tau=I\alpha$

I is moment of inertia of disk, $I=\dfrac{mr^2}{2}$

$\tau=\dfrac{mr^2\alpha }{2}\\\\\tau=\dfrac{1.1\times (0.09)^2\times 73.3 }{2\times 42.4}\\\\\tau=7.7\times 10^{-3}\ N-m$

So, the frictional torque exerted on the grindstone is  $7.7\times 10^{-3}\ N-m$.