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?

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

ConcepcionPetillo ConcepcionPetillo · Answer 2 · 2022-03-24T13:25:27+01:00

The time taken to reach the angular speed of 1600 rpm is 0.76s

Rotational motion:

Given that the angular acceleration of the wheel is:

α = 220 rad/s²

Initial angular speed ω₀ = 0

Final angular speed ω = 1600 rpm

ω = 1600×2π/60 rad/s

ω = 167.46 rad/s

Now, from the first equation in rotational motion:

ω = ω₀ + αt

here, t is the time taken

167.46 = 0 + 220×t

t = 167.46 / 220

t = 0.76 s

After 0.76 seconds the angular speed becomes 167.46 rad/s

Learn more about rotational motion:

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