Question

at what speed in miles per hour will a bicycle travel if the rider can cause the 26 inch diameter wheel to rotate 90 revolutions per minute?

Answer 1

\[v = r \omega\]\[\omega = angular\ velocity\ (rad/s)\]

1 rpm = 2pi/60 rad/second

90 rpm = 3pi rad/s

answer is v = 26*3pi = 78pi inch/s

Answer 2

( (26 \[Pi])/12 * 90 * 60 )/5280 = 6.96148 mph