Question

A bicycle with 24-inch diameter wheels is traveling at 15 mi/h. Find the angular speed of the wheels in rad/ min. How many revolutions per minute do the wheels make?

Answer 1

ω = 1320 rad/min, Revolution per minutes = 210.0845

Step-by-step explanation:

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

To Find:

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