SOLUTION: The diameter of each wheel of a bicycle is 27 inches. You are traveling at a speed of 22 miles per hour on this bicycle. - What is the angular speed of the wheels in radians per

Algebra ->  Trigonometry-basics -> SOLUTION: The diameter of each wheel of a bicycle is 27 inches. You are traveling at a speed of 22 miles per hour on this bicycle. - What is the angular speed of the wheels in radians per       Log On


   



Question 1157685: The diameter of each wheel of a bicycle is 27 inches. You are traveling at a speed
of 22 miles per hour on this bicycle. - What is the angular speed of the wheels in radians per minute? Is there a way to do this without first finding the revolutions per minute of the wheels?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find out how many inches / min it takes
for the wheel to trace out one revolution
( one circumference ) on the ground.
[ miles / hr ] x [ hrs / min ] x [ ft / mile ] x [ inches / ft ] = [ inches / min ]
+22%2A%28+1%2F60+%29%2A%28+5280+%2F+1+%29%2A%28+12+%2F+1+%29+=+1393920+%2F+60+
+1393920+%2F+60+=+23232+ inches / min linear speed
-------------------
Let +C+ = circumference of the wheel
+C+=+2%2Api%2A%28+27%2F2+%29+
+C+=+27pi+
+C+=+84.823+ inches
------------------------------
For angular speed:
[2pi radians / C ] x [ C / min ] = [ radians / min ]
+%28+2pi+%2F+84.823+%29%2A%28+23232+%2F+1+%29+=+145970.96+%2F+84.823+
++145970.96+%2F+84.823+=+1720.89+
1,720.89 radians/min
-----------------------------
check:
+1720.89+%2F+%28+2pi+%29+=+273.89+ rev/min
[ in / rev ] x [ rev / min] = in / min ]
+%28+84.823+%2F+1+%29%2A%28+273.89+%2F+1+%29+=+23232+ in / min
You can finish this
This is the only way I know to do this
You may want a 2nd opinion, too