Question

If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.

Answer 1

Check the picture,

let A be the point where the circle (the wheel) touches the ground. One revolution is completed when A is back on the ground. This happens after all the points in the circumference, have touched the ground.

So one revolution means 1 circumference, which is equal to one 2πR.

50 revolutions per minute means the velocity is 50*2πR inches per 1 minute.

50*2πR=50*2*3.14*80 (inches) = 25,120 inches per minute.

1 foot is 12 inch, so 25,120 inches are
`(25,120)/(12) =2093.3` feet

1 mile is 5280 feet so 2093.3 feet are
`(2093.3)/(5280)= 0.4` mile

now we convert minutes to hour: 1 hour = 60 min, so 1 min=1/60 hour

finally:

velocity=
`(0.4miles)/(1/60 hours)= 0.4*60 mi/h=4*6 mi/h= 24 mi/h`