A Ferris wheel rotates at an angular velocity of 0.28 rad/s. Starting from rest, it reaches its operating speed with an average angular acceleration of 0.021 rad/s2. How long does it take the wheel to come up to operating speed?

ω2=ω1)+angular acceleration*time

or
time = (ω2-ω1)/angular acceleration
=(0.28-0)/0.021
=40/3 sec.

To find the time it takes for the Ferris wheel to come up to operating speed, we can use the formula:

Δω = ωf - ωi

where Δω is the change in angular velocity, ωf is the final angular velocity, and ωi is the initial angular velocity.

First, let's find the initial angular velocity. Since the Ferris wheel starts from rest, the initial angular velocity (ωi) is 0 rad/s.

Second, let's find the final angular velocity. The question states that the Ferris wheel reaches its operating speed (ωf) with an average angular acceleration (α) of 0.021 rad/s^2. We can use the formula:

α = (ωf - ωi) / t

where t is the time it takes to reach the final angular velocity.

Rearranging the formula, we have:

ωf - ωi = α * t

Substituting the known values, we have:

0.28 rad/s - 0 rad/s = 0.021 rad/s^2 * t

0.28 rad/s = 0.021 rad/s^2 * t

Now, let's solve for t:

t = 0.28 rad/s / 0.021 rad/s^2

t ≈ 13.33 s

Therefore, it takes approximately 13.33 seconds for the Ferris wheel to come up to operating speed.