An old wheat-grinding wheel in a museum actually works. The sign on the wall says that the wheel has a rotational acceleration of 220 rad/s2 as its spinning rotational speed increases from zero to 1600 rpm. How long does it take the wheel to attain this rotational speed?

0.76 s

Explanation:

We use the formula for rotational speed, ω given its rotational acceleration α. ω = ω₀ + α (t - t₀) where ω₀ = initial rotational speed, ω = final rotational speed, ω₀ = initial rotational speed, α = rotational acceleration and t = initial time and t₀ = final time.

Since the wheel starts from rest, ω₀ = 0 and t₀ = 0. Given that α = 220 rad/s² and ω = 1600 rpm = 1600 * 2π/60 rad/s = 167.55 rad/s. Substituting these values into the equation ω = ω₀ + α (t - t₀)

167.55 = 0 + 220 (t - 0) = 220t

So, t = 167.55/220 = 0.762 s ≅ 0.76 s

So, it takes the wheel 0.76 s to attain this rotational speed