Question

A Ferris wheel completes 6 revolutions in 12 minutes. The radius of the Ferris wheel is 40 feet.

What is the linear velocity of the ferris wheel in inches per second?

Answer 1

25.13 inches per second

Explanation:

The formula for linear velocity is:

`v=(2\pi r)/(T)`

Where
`r` is the radius, and
`T` is the period of oscilation.

The radius is:

`r=40feet` but because we need the answer in inches per second we need to convert this to inches (1 feet = 12 inches):

`r=40*12in\\r=480in`

and the Period is the time it takes to complete a revolucion:

`T=(12minutes)/(6revolutions)\\ T=2minutes/revolution`

it takes 2 minutes to complete 1 revolution. Again, since we need the result in inches per second we need to convert the Period to seconds (1 minute = 60 seconds)

`T=2*60seconds/revolution\\T=120seconds/revolution`

substituting our values for the linear velocity:

`v=(2\pi r)/(T)`

`v=(2\pi (480inches))/(120seconds) \\v=25.13inches/second`

the linear velocity is 25.13 inches per second