Question

On a ferris wheel, Sarah observes that it takes 45 seconds for her chair to complete a full revolution. Her chair is 30 feet from the axle of the ferris wheel.

To the nearest hundreth, Sarah's angular velocity is _____ radians per minute.

Answer 1

The angular velocity is 8.38 radians per minute

Explanation:

From the question,

It takes 45 seconds to complete a full revolution,

That is, 1rev/45secs

First, we will convert this to revolutions per minute (rev/min)

1rev/45secs =
`(1 revolutions)/(45 seconds) * (60seconds)/(1minute)`

= 4/3 rev/min

Now, we will convert this to radians per minute (rad/min)

1 revolutions = 2π rad

4/3 rev/min =
`((4)/(3) rev)/(min) * (2\pi rad)/(1 rev)`

= 8.38 rad/min

Hence, the angular velocity is 8.38 radians per minute