You have a grindstone (a disk) that is 105.00 kg, has a 0.297-m radius, and is turning at 71.150 rpm, and you press a steel axe against it with a radial force of 46.650 N. Assuming the kinetic coefficient of friction between steel and stone is 0.451. How many turns will the stone make before coming to rest?

3.27 turns

Explanation:

To find how many turns (θ) will the stone make before coming to rest we will use the following equation:

Where:

: is the final angular velocity = 0

: is the initial angular velocity = 71.150 rpm

α: is the angular acceleration

First, we need to calculate the angular acceleration (α). To do that, we can use the following equation:

Where:

I: is the moment of inertia for the disk

τ: is the torque  

The moment of inertia is:

Where:

m: is the mass of the disk = 105.00 kg

r: is the radius of the disk = 0.297 m

Now, the torque is equal to:

Where:

F: is the applied force = 46.650 N      

μ: is the kinetic coefficient of friction = 0.451

The minus sign is because the friction force is acting opposite to motion of grindstone.    

Having the moment of inertia and the torque, we can find the angular acceleration:

Finally, we can find the number of turns that the stone will make before coming to rest:

I hope it helps you!

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