Question

A car is traveling at a speed of 57 mph. The radius of its tires are 17 inches. What is the angular speed of the tires in radians/minutes? Round to the nearest whole number and enter the number only.

Answer 1

3541 radian/minutes

Step-by-step explanation:
`\begin{gathered} \text{Speed of the car = }57\text{mph} \\ \text{radius of the tires = 17 inches} \\ \\ We\text{ n}eed\text{ to find the angular speed} \end{gathered}`

To find angular speed, we will apply the formula:

`\begin{gathered} speed\text{ = r}\omega \\ \text{where r = radius } \\ \omega\text{ = angular sp}eed \end{gathered}`

The units of the speed and the radius are not the same. We need them to be in the same unit.

So we will convert the speed to inches per minute:

`\begin{gathered} \text{speed = 57 miles per hour} \\ 1\text{ mile = 5280ft} \\ 1\text{ ft = 12 inches} \\ 1hour\text{ = 60 minutes} \\ \text{Conversion:} \\ 57\text{ }(miles)/(hr)*\frac{5280\text{ ft}}{1\text{ mile}}*\frac{12\text{ inches}}{1\text{ ft}}*\frac{1\text{ hour}}{60\text{ mins}} \end{gathered}`

Simplifying:

Let's substitute the our values into the equation relating the angular speed:

`\begin{gathered} speed\text{ = r}\omega \\ 60192\text{ }\frac{\text{Inches}}{\min s}\text{= 17 inches }*\text{ }\omega \\ \text{divide both sides }by\text{ 17:} \\ \frac{60192\text{ }}{17\text{ inches}}\frac{\text{Inches}}{\min s}\text{ = }\omega \\ w\text{ = }\frac{60192\text{ radians}}{17\text{ mins}}\text{ (radians as a result of the angle)} \\ w\text{ = 3540.71} \\ \\ To\text{ the nearest whole number, angular sp}eed\text{ is 3541 radians/minutes} \end{gathered}`