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/
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