Math CentralQuandaries & Queries


Question from Kay:

A wheel with a radius of 7 inches is rotating at 4 revolutions per second. What is the
linear speed v, in feet per second?

Hi Kay,

Suppose the wheel touches the road at a point $P.$ I put a mark, red dot, on the wheel just where it touches the ground.


Roll the wheel along the road until the red dot touches the ground again at the point $Q.$ The distance along the road from $P$ to $Q$ in feet, $|PQ|,$ is the circumference of the wheel. The wheel rotates at 4 revolutions per second so the wheel has travelled $|PQ|$ feet in a quarter of a second. How far will it travel in a second?


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