Answer:
The angular speed is 3,227 rad/min
Step-by-step explanation:
Remember that
1 mile=63,360 inches
step 1
Find the circumference of the wheels
The circumference is equal to
[tex]C=\pi D[/tex]
we have
[tex]D=36\ in[/tex]
substitute
[tex]C=\pi (36)[/tex]
[tex]C=36\pi\ in[/tex]
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
[tex]\frac{36\pi }{2\pi }=\frac{58,080}{x} \\\\x=2*58,080/36\\\\x=3,226.67 \ rad[/tex]
therefore
The angular speed is 3,227 rad/min
