A Ferris wheel rotates at an angular velocity of 0.20 rad/s. Starting from rest, it reaches its operating speed with an average angular acceleration of 0.029 rad/s2. How long does it take the wheel to come up to operating speed?
(final angular velocity)/(angular acceleration) = 0.20/0.029 = ___ seconds
. 0.71 T
To find the time it takes for the ferris wheel to come up to operating speed, we need to use the equation of motion in rotational kinematics:
ω = ω0 + αt
where:
ω = final angular velocity (operating speed) = 0.20 rad/s
ω0 = initial angular velocity (rest) = 0 rad/s
α = average angular acceleration = 0.029 rad/s^2
t = time
We need to solve for t. Rearranging the equation, we have:
t = (ω - ω0)/α
Substituting the given values, we get:
t = (0.20 rad/s - 0 rad/s)/(0.029 rad/s^2)
Calculating the expression:
t = 0.20 rad/s / 0.029 rad/s^2
Simplifying:
t ≈ 6.897 s
Therefore, it takes approximately 6.897 seconds for the ferris wheel to come up to operating speed.