A truck with 36-in.-diameter wheels is traveling at 55 mi/h.Find the angular speed of the wheels in rad/min

Accepted Solution

Answer:The angular speed is 3,227 rad/minStep-by-step explanation:Remember that1 mile=63,360 inchesstep 1Find the circumference of the wheelsThe 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 2we know thatThe speed of the wheel is 55 mi/hConvert to mi/min55 mi/h=55/60 mi/minConvert to in/min(55/60) mi/min=55*63,360/60 in/min= 58,080 in/minwe know thatThe circumference of the wheel subtends a central angle of 2Ο€ radianssousing proportionFind 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]thereforeThe angular speed is 3,227 rad/min