Question

if a wheel with a diameter of 30 inches spins at a rate of 40 revolutions per minute, find the approximate linear velocity in miles per hour. use pi. 3.14 determine the linear velocity of an object with an angular velocity of 8.9 radians per second at a distance of 20 centimeters from the center. use pi 3.14

Answer 1

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

ω = 40 revolutions per minute.  1 minute = (1/60) hour.

= 40*2π radians / (1/60) hour = 4800π radians per hour          π = 3.14

= 4800*3.14 = 15072 radians / hour

but radius, r = 30 inches,  63360 inches = 1 mile,  30 inches = (30/63360) mile  

Linear velocity, v = ωr

                       v = 15072 radians / hour *  (30/63360) mile  
                       v ≈  7.136 miles / hour

b) Linear velocity, v = ωr
                           v = 8.9 radians/second * 20 cm
                           v = 178 cm/s