Question

a ferris wheel rotates at an angular velocity of 0.29 rad/s. starting from rest, it reaches its operating speed with an average angular acceleration of 0.035 rad/s2. how long does it take the wheel to come up to operating speed?

Answer 1

To find the time it takes for the ferris wheel to come up to operating speed, we can use the following kinematic equation for rotational motion:

ω = ω0 + αt

where:
ω is the final angular velocity (operating speed),
ω0 is the initial angular velocity (rest),
α is the angular acceleration, and
t is the time.

Given:
ω = 0.29 rad/s (operating speed)
ω0 = 0 rad/s (initial angular velocity, starting from rest)
α = 0.035 rad/s² (average angular acceleration)

Plugging in the values into the equation, we have:

0.29 rad/s = 0 rad/s + 0.035 rad/s² * t

Simplifying the equation, we get:

0.29 rad/s = 0.035 rad/s² * t

Now, we can solve for t by isolating it:

t = 0.29 rad/s / 0.035 rad/s²

Evaluating the expression, we find:

t ≈ 8.286 seconds

Therefore, it takes approximately 8.286 seconds for the ferris wheel to come up to its operating speed.