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