Calculate the angular velocity in radians per minute of a Ferris wheel 250 ft in diameter that takes 45 s to rotate once. Express the answer in terms of `pi` . Thank you to anyone who helps!

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lemjay | High School Teacher | (Level 3) Senior Educator

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The formula of of angular velocity is:

`omega=theta/t`

where
`omega` - angular velocity

`theta` - angle of rotation

`t` - time

Since it takes 45 seconds to rotate once, then `theta = 2pi` . And, converting the time to minutes, then the value of t is:

`t= 45 sec * (1 min)/(60 sec)= 3/4`

So,

`omega = (2pi)/(3/4)=2pi*(4/3)=(8pi)/3`

Hence, the angular velocity is `(8pi)/3` radian per minute.

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