Answer:
3.27 turns
Explanation:
To find how many turns (θ) will the stone make before coming to rest we will use the following equation:
<u>Where:</u>
: is the final angular velocity = 0
: is the initial angular velocity = 71.150 rpm
α: is the angular acceleration
<em>First, we need to calculate the </em><em>angular acceleration (α)</em><em>. To do that, we can use the following equation:</em>
<u>Where:</u>
I: is the moment of inertia for the disk
τ: is the torque
The moment of inertia is:
<u>Where:</u>
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:
<u>Where:</u>
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!