Answer :
Final answer:
Using principles of rotational motion and constant angular acceleration, the grindstone turns through an angle of 32.0 rad during the given time interval.
Explanation:
In this problem about rotational motion, we will use the formula for angular displacement under constant acceleration, expressed as = ωi*t + 0.5*α*t^2, where ωi is the initial angular speed, α is the angular acceleration, and t is the time.
First, we need to calculate the angular acceleration (α). We're given that the grindstone increases its angular speed from 4.00 rad/s to 12.00 rad/s in 4.00 s. Angular acceleration is defined as the change in angular velocity divided by time, therefore α = (ωf - ωi) / t = (12.00 rad/s - 4.00 rad/s)/4.00s = 2 rad/s^2.
Substituting these values into our formula for , we get = (4.00 rad/s * 4.00 s) + 0.5 * 2 rad/s^2 * (4.00 s)^2 = 16 rad + 16 rad = 32.0 rad.
So, the grindstone turns through an angle of 32.0 rad during the given time interval.
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