Q. 51 - Precalculus Enhanced with Graphing Utilities

Question

Angular Speed of a Race Car A race car is driven around a circular track at a constant speed of $180$ miles per hour. If the diameter of the track is $\frac{1}{2}$ mile, what is the angular speed of the car? Express your answer in revolutions per hour (which is equivalent to laps per hour).

Step-by-Step Solution

Answer

The angular speed is $114.59$ revolutions per hour

Step 1: Given information

Given the car speed as $180 miles/hr$ and diameter of the track is $\frac{1}{2}mile$

Step 2: Use the formula for angular speed and calculate

Calculating, we get

$$\begin{gathered} v=r\omega \\ \omega =\frac{v}{r} \\ \omega =\frac{180\mathrm{mi}/\mathrm{hr}}{0.25\mathrm{mi}} \\ \omega =720\frac{\mathrm{rad}}{\mathrm{hr}}·\frac{1\mathrm{rev}}{2\pi \mathrm{rad}} \\ \omega =114.59\frac{rev}{hr} \end{gathered}$$