Circumference and Rotation

Date: 10/07/2003 at 09:44:58
From: Liz  
Subject: radius

The wheel on a truck rotates 330 times in a mile.  Find the radius of 
the tire using C=2(pi)r.

Is 330 a clue to finding the radius?  Is the one mile a factor in this
problem?  Is there enough info to find the radius?

Date: 10/07/2003 at 11:44:02
From: Doctor Douglas
Subject: Re: radius

Hi Liz,

Yes, the 330 is a big clue--it tells you how many times the wheel goes
around when the truck travels one mile.  This means that each time the
wheel goes around once, the truck travels 1/330th of a mile along the
road.

This distance (1/330) is the circumference C of the tire, because as
the truck moves this distance, the wheel goes around once.  In each
rotation of the wheel, every point on the circumference of the tire
touches the ground once.  Therefore, at the end of one rotation, the
truck has moved (along the ground) a distance of the circumference. 
This is the crucial fact that allows you to solve the problem.

Note that we also need to make one other assumption about this
problem:  we need to know that the wheel doesn't slip on the ground,
as for example, it might if the truck were driving on ice.  This fact
was not spelled out in the problem, but it is a reasonable assumption
that I think we are allowed to make.

Now that you know the circumference, can you use the formula you were
given to figure out the radius? 

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/