Chapter 4.1, Problem 45E

Solution

To identify: The how many revolutions per minute are her wheels making. Bicycle Racing 2016 Olympics gold medalist Mariana Pajón races on a BMX bike with 10-in.-radius wheels. When she is traveling at a speed of 24 ft/sec.

The revolutions per minute are her wheels making is $275.02\text{rpm}$

Given information Bicycle Racing 2016 Olympics gold medalist Mariana Pajón races on a BMX bike with 10-in.-radius wheels. When she is traveling at a speed of 24 ft/sec.

Explanation:

Consider the given information

One revolution is equal to the circumference of the wheel:

  $2\pi r=2\pi \left(10\right)=20\pi$ inches per revolution.

In feet,

  $20\pi \text{inches}\times \frac{\text{1ft}}{\text{12in}}=\frac{5\pi }{3}\text{ft/rev}$ .

Divide the speed by the circumference to find the number of revolutions per second.

  $\frac{\text{24ft/sec}}{\frac{5\pi }{3}\text{ft/sec}}=\frac{72}{5\pi }\text{rev/sec}$ .

Convert second to minutes:

  $\begin{array}{c}\frac{72}{5\pi }\text{rev/sec}\times \frac{60\sec }{1\min }=\frac{864}{\pi }\\ \frac{864}{\pi }\approx 275.02\text{rpm}\end{array}$