A bicycle with 26-inch diameter wheels is traveling at 20 mi/h. Find the angular speed of the wheels in rad/min.
______radians per minute
___revolutions per minuteω = 1320 rad/min, Revolution per minutes = 210.084
Diameter = 24 in
Radius r = 24/2 in = 12 in = 12 × 2.54 cm = 30.48 cm = 0.3048 m
Linear Speed v= 15 mi/hr = 15 * 1609.34 / 3600 m/s = 6.7056 m/s
Angular Speed ω = v / r = (6.7056 m/s) / (0.3048 m) = 21.999945
ω = 22 rad/s = 22× 60 rad/min = 1320 rad/min
∴ 1 revolution = 2π rad
⇒1 rad = 1 / 2π rev
so 1320 rad/min = 1320 / 2π rev/min = 210.0845 rev/min
Revolution per minutes = 210.0845
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