# Reversing angular and linear formulas to find rpm.

## Homework Statement

A simple model of the core of a tornado is a right circular cylinder that rotates about its axis. If a tornado has a core diameter of 200 feet and maximum wind speed of 240 mi/hr (or 352 ft/sec) at the perimeter of the core, approximate the number of revolutions the core makes each minute. (Round your answer to one decimal place.)

## Homework Equations

s=r(theta) and V=r(omega)

## The Attempt at a Solution

The practice problems had a radius and rpm given and I could find the angular and linear speeds, where I'm struggling is I'm not sure how to reverse the example in order to convert the speed and radius into rpm.

V=r(omega) then (omega)=V/r ???is that right? then when I plug the numbers:
somewhere I'm sure pi has to come in, 2pi=1rpm...so do I multiply by 1/2pi ??? this is where I'm getting lost.

BruceW
Homework Helper
Now you must remember what the definition of omega is - it is the angular frequency, and it is given by the equation:
$$\omega = 2 \pi f$$
(where f is frequency). So using this you can calculate the frequency in units of 1/seconds. Then, the question asks for it in units of 1/minutes, so you do the unit conversion to get that.

BruceW
Homework Helper
It looks like my latex isn't working, but you can see what the equaton is anyway.

BruceW
Homework Helper
just to make sure: omega = 2pi times f