Question

A truck with 36-in.-diameter wheels is traveling at 55 mi/h.

Find the angular speed of the wheels in rad/min

Answer 1

The angular speed is 3,227 rad/min

Explanation:

Remember that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

The circumference is equal to

`C=\pi D`

we have

`D=36\ in`

substitute

`C=\pi (36)`

`C=36\pi\ in`

step 2

we know that

The speed of the wheel is 55 mi/h

Convert to mi/min

55 mi/h=55/60 mi/min

Convert to in/min

(55/60) mi/min=55*63,360/60 in/min= 58,080 in/min

we know that

The circumference of the wheel subtends a central angle of 2π radians

so

using proportion

Find out how much radians are 58,080 inches

`(36\pi )/(2\pi )=(58,080)/(x) \\\\x=2*58,080/36\\\\x=3,226.67 \ rad`

therefore

The angular speed is 3,227 rad/min