Question

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?

Answer 1

Answer:

t = 9.25 s

Explanation:

Given that,

Initial angular velocity, $\omega_o=0$ (at rest)

Final angular velocity, $\omega_o=0.25\ rad/s$

Angular acceleration, $\alpha =0.027\ rad/s^2$

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 :

$\alpha =\dfrac{\omega_f-\omega_o}{t}\\\\t=\dfrac{\omega_f-\omega_o}{\alpha }\\\\t=\dfrac{0.25-0}{0.027}\\\\t=9.25\ s$

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