A Ferris wheel rotates at an angular velocity of 0.25 rad/s. Starting from rest, it reaches its operating speed with an average angular acceleration of 0.027 rad/s2. How long does it take the wheel to come up to operating speed?

t = 9.25 s

Explanation:

Given that,

Initial angular velocity, (at rest)

Final angular velocity,

Angular acceleration,

We need to find the time it take the wheel to come up to operating speed. We know that the angular acceleration in terms of angular speed is given by :

So, it will reach up to the operating speed in 9.25 s.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y