Question

if a wheel with a diameter of 10 feet spins at a rate of 5 revolutions per minute, find the approximate linear velocity in miles per hour use pi. 3.14

Answer 1

A) Linear velocity, v = ωr           ω = Angular velocity, r = radius.

ω = 5 revolutions per minute.  1 minute = (1/60) hour. 

= 5*2π radians / (1/60) hour = 600π radians per hour          π = 3.14 

= 600*3.14 = 1884 radians / hour

but radius, r = 10 feet,  5280 feet = 1 mile,  10 feet = (10/5280) mile   

Linear velocity, v = ωr

                       v = 1884 radians / hour *  (10/5280) mile   
                       v ≈  3.568 miles / hour