Question

How do you convert 16 revolutions to radians?

Answer 1

You can see that `2pi` radians becomes one revolution when you use the arc length formula:

`s = rtheta`

Let `theta = 2pi`. That means:

`color(green)(s = C = 2pir)`

which is the formula for the full circumference of a circle. Since `2pi` radians is one revolution:

`16 cancel"rev" xx ((2pi " rad")/(1 cancel"rev")) = color(blue)(32pi " rad")`