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 $\frac{25,120}{12} =2093.3$ feet

1 mile is 5280 feet so 2093.3 feet are $\frac{2093.3}{5280}= 0.4$ mile

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

finally:

velocity= $\frac{0.4miles}{1/60 hours}= 0.4*60 mi/h=4*6 mi/h= 24 mi/h$