First of all, let's follow the suggestion given by the question and convert the speed of the truck from mi/h to in/min. We know that 1 mile is equivalent to 63360 inches and 1 hour is equivalent to 60 minutes. Then 55 mi/h is equivalent to:
[tex]55\text{ }\frac{mi}{h}=55\text{ }\frac{63360in}{60min}=55\cdot\frac{63360}{60}\frac{in}{min}=58080\frac{in}{min}[/tex]So we know that the truck travels 58080 inches in a minute. If we divide this distance by the circumference of the wheels we'll find the number of revolutions performed by them in a minute. The wheels have a 30 in diameter and since the circumference of a circle is given by the product between π and its diameter we have that the circumference of the wheels is:
[tex]\pi\cdot30in=30\pi in[/tex]Then the number of revolutions performed by each wheel in a minute is:
[tex]\frac{58080}{30\pi}=1936\pi[/tex]These are the rpm asked in the second question. This result can be used to solve the first part since we know that a revolution is performed when the wheels rotate 2π radians. This means that if we multiply the rpm by 2π we'll find the angular speed of the wheels in rad/min:
[tex]1936\pi\cdot2\pi=3872\pi^2[/tex]AnswerNow that we found the quantities requested we should express them as decimal numbers rounded to 1 decimal place.
The first answer is: 38215.1 rad/min
The second answer is 6082.1 rpm
