Question

A bicycle wheel with a diameter of 24 inches is rotating 3 revolutions per second. What is the linear speed in feet/sec? Use 3.14 for pi and round to the nearest tenth

Answer 1

`18.8ft\/s`

Step-by-step explanation

We want to find the linear speed of the bicycle in feet per second.

First, we have to find the circumference of the bicycle wheel (in feet).

The circumference of a circle is:

`C=\pi\cdot D`

First, convert the diameter to feet:

`\begin{gathered} 12in=1ft \\ \Rightarrow24in=(24)/(12)=2ft \end{gathered}`

Hence, the circumference of the wheel is:

`\begin{gathered} C=3.14\cdot2 \\ C=6.28ft \end{gathered}`

This implies that each revolution is an equivalent linear distance of 6.28 ft i.e 6.28 feet per revolution.

To find the linear speed, we have to find the product of the circumference and the

rotational speed. That is:

`\begin{gathered} s=6.28(ft)/(rev)\cdot3(rev)/(\sec ) \\ s=18.84ft\/s \\ s\approx18.8ft\/s \end{gathered}`

That is its linear speed.