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An electric grinder is spinning counterclockwise at 37 rev/s. When the power is turned off, the grinder slows at a steady rate, taking 71 seconds to stop rotating. How many revolutions did it make while slowing to a stop?

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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