Answer :
The electric grinder made 18.5 revolutions while slowing to a stop.
To find the number of revolutions the electric grinder made while slowing to a stop, we can use the equations of rotational motion.
Given:
Initial angular velocity (ω₀) = 37 rev/s
Time taken to stop (t) = 71 s
First, let's calculate the angular acceleration (α). We know that the change in angular velocity (Δω) is equal to the negative initial angular velocity (ω₀) because the grinder stops rotating.
Δω = -ω₀ = -37 rev/s
We can use the equation for angular acceleration:
α = Δω / t = -37 rev/s / 71 s
Now, let's use the equation for the change in angle (Δθ) or the number of revolutions:
Δθ = ω₀ * t + (1/2) * α * t²
Plugging in the values:
Δθ = 37 rev/s * 71 s + (1/2) * (-37 rev/s / 71 s) * (71 s)²
Simplifying the expression:
Δθ = 37 rev + (-18.5 rev) = 18.5 rev
Therefore, the electric grinder made 18.5 revolutions while slowing to a stop.
Learn more about acceleration here: https://brainly.com/question/2303856
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