You have a grindstone (a disk) that is 90.0 kg, has a 0.340-m radius, and is turning at 90.0 rpm, and you press a steel axe against it with a radial force of 20.0 n.
(a) assuming the kinetic coefficient of friction between steel and stone is 0.20, calculate the angular acceleration of the grindstone.
(b) how many turns will the stone make before coming to rest?

Explanation:

It is given that,

Mass of the grindstone, m = 90 kg

Radius of the disk, r = 0.34 m

Angular speed of the disk,

Radial force acting on the disk, F = 20 N

(a) The kinetic coefficient of friction between steel and stone is 0.2. The torque due to frictional force is given by :

The relationship between the torque and the angular acceleration is given by :

, I is the moment of inertia of the disk

(b) Let are the number of turns make by the stone. Using the  equation of rotational kinematics to find it as :

Hence, this is the required solution.

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