Question

What is the linear speed in miles per hour of the tip of a lawnmower blade spinning at 2300 revolutions per minute in a lawnmower that cuts a path that is 28 inches wide?

Answer 1

191.59 mile/hour is the linear speed of the tip of a lawnmower blade.

Explanation:

`v=r* \omega`

v = linear speed

r = radius of circular path

`\omega` = Angular speed

We have:

Revolution of blade in a minute = 2300

1 hour = 60 min

Revolution in 1 hour or 60 min = 2300 × 60 =138000 revolution per hour

Angular speed of blade =

`\omega =138000 * 2\pi=867,079.57 rad/hour`

Width or diameter of the blade = d = 28 cm

Radius of blade =
`(28 inch)/(2)=14 inch`

1 mile = 63360 inch

`14 inch=(14)/(63360) mile`

Linear speed of the blade: v

`v=867,079.57 rad/hour* (14)/(63360) mile=191.59 mile/hour`

191.59 mile/hour is the linear speed of the tip of a lawnmower blade.