Difference in Radius, Difference in Speed

Date: 06/25/2002 at 15:24:41
From: Stacey Freeman
Subject: Diameter effects rotational speed

The diameter of a tire is 56 cm, and the valve stem is 17 cm from the
center.  What is the difference between the speed of a point on the
tread of the tire and the speed of another point on the valve stem
when the car wheel is moving at 5000 rpm?  Can you show me the steps
to solve this problem?

Date: 06/25/2002 at 20:49:14
From: Doctor Ian
Subject: Re: Diameter effects rotational speed

Hi Stacey,

Suppose we have a disc whose radius is 10 cm, and it's rotating 
at 1000 rpm.  How fast is a point on the edge of the disc moving?

The circumference of the disc is pi times the diameter, 

  circumference = pi * (2 * 10 cm)

Each time the disc rotates, a point on the edge travels a 
distance equal to the circumference of the disc.  So in 1 minute, 
a point travels 1000 times the circumference:

  distance in 1 minute = 1000 * pi * (2 * 10 cm)

                       = pi * 20000 cm

                       = pi * 200 m

or about 600 meters.  So the speed of that point is 600 meters 
per minute. 

Can you take it from here?

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