SOLUTION: A truck with 30inch diameter wheels is traveling at 55mi/h. Find the angular speed of the wheels in radians per minute? And how many revolutions per minute do the wheels make?

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Question 1045458: A truck with 30inch diameter wheels is traveling at 55mi/h. Find the angular speed of the wheels in radians per minute? And how many revolutions per minute do the wheels make?
Found 2 solutions by josmiceli, advanced_Learner:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Convert mi/hr to in/min
[ 55 mi/hr ] x [ 1/60 hr/mins ] x [ 5280 ft/mi ] x [ 12 in/ft ]
+55%2A%28+1%2F60+%29%2A5280%2A12+=+58080+ in/min
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How many times does the circumference, C, of the
wheel go into this number?
+C+=+2%2Api%2A30+
+C+=+60%2Api+
------------------
[ in / min ] / [ in/C ] = [ C/min ]
+58080+%2F+%28+60%2Api+%29+=+968%2Fpi+ C/min
and
[ C/min ] x [ radians/C ] = radians/min ]
+%28+968%2Fpi+%29%2A%28+2%2Api+%29+=+1936+ radians/min
The angular speed of the wheels is 1,936 radians/min
----------------------
[ revolutions/min ] = [ radians/min ] x [ 1C/radians ]
+1936%2A%28+1%2F%282%2Api%29+%29+=+308.124+
The wheel makes 308.124 revs/min
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Check my math & get a 2nd opinion, too




Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
A truck with 30inch diameter wheels is traveling at 55mi/h. Find the angular speed of the wheels in radians per minute? And how many revolutions per minute do the wheels make?


convert 55 miles per hour into in/min
the wheel is rotating 55%2A5280%2A12%2F%2860%29=58080 in/min

C=d%2Api
C=30%2Api inches
So, there are 30%2Api inches per revolution of the wheel.

58080=30%2Api
(in/min)/(inc/rev)=rev/min
58080%2F%2830%2Api%29=1936%2F%28pi%29 rev/min
angular speed
(x*rev/min)*(rad/rev)=(rad/min)

2pi%2F%281%29*1936%2F%28pi%29=3872 rad/min first part answer