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

t = 9.25 s

Step-by-step 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 =(\omega_f-\omega_o)/(t)\\\\t=(\omega_f-\omega_o)/(\alpha )\\\\t=(0.25-0)/(0.027)\\\\t=9.25\ s`

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