Linear Velocity

Question

What is the linear velocity in MILES PER HOUR of the tip of a lawnmower blade spinning at 2200 revolutions per minute in a lawnmower that cuts a path that is 16 inches wide?

 

 

I can't seem to get the conversions right for this question. Any help is appreciated. Thanks in advance!

Answer 1

Hi Gregory,

The angular velocity is

f = 2200rpm = (2200 rev/min)(60 min/hr) = 1.32x10⁵ rev/hr

ω = 2π f

   = 8.2938x10⁵ rad/hr

The width of the path is the diameter of the circle centered at the midpoint of the blade, R = 16/2 inches

R = (8 in)(1/36 yard/1 in)

  =(2/9 yard)(1mile/1760yards)

  = 1.2626x10^-4 mile

V = ω R

   =8.2938x10⁵ rad/hr * 1.2626x10^-4 mile 

   = 105 miles/hour