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# Angular and Linear Velocities

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Calculate angular speed of the 26 inch bicycle rotating at 200 revolutions per minute. Express your answer in radians per minute. Use pi.

Apr 2, 2015

#3
+101149
+5

I'm assuming that 20 inches represents the diameter, so 10 inches is the radius

15.5 miles in one hour = 15.5 x 5280 ft  = 81840 ft / 60min = 1364 ft/min

And the bike travels [2 * pi * 10] inches =  (20 * pi) inches  = 62.83 inches in every revolution  = about 5.236 ft in every revolution

So.........1364/5.236 = about 260.5 revolutions per minite = 261 revs (rounded)

Apr 6, 2015

#1
+101149
+5

Well, if it rotates at 200 revolutions  per minute, there are 2pi radians in each revolution....so....it goes through 200 x 2pi   = 400pi rads/  min  ..... the tire size is irrelevant in terms of angular speed......

Apr 2, 2015
#2
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at what rate would you have to pedal a 20 inch bike so that it traveled at a linear speed of 15.5 miles per hour? express your answer in revolutions per minute rounded to the nearest whole number. (Hint: first change miles per hour into inches per minute)

Apr 6, 2015
#3
+101149
+5

I'm assuming that 20 inches represents the diameter, so 10 inches is the radius

15.5 miles in one hour = 15.5 x 5280 ft  = 81840 ft / 60min = 1364 ft/min

And the bike travels [2 * pi * 10] inches =  (20 * pi) inches  = 62.83 inches in every revolution  = about 5.236 ft in every revolution

So.........1364/5.236 = about 260.5 revolutions per minite = 261 revs (rounded)

CPhill Apr 6, 2015