Question

A lawnmower blade has a diameter of 30 inches. If the blade rotates at a speed of 126 revolutions per minute, find the linear speed of the tips of the blade in feet per second.

Answer 1

The relationship between linear speed and angular speed is given by:

`\begin{gathered} \omega=(v)/(r) \\ where\colon \\ \omega=Angular_{\text{ }}sped \\ v=Linear_{\text{ }}speed \\ r=radius \end{gathered}`

so:

`\begin{gathered} r=30in=0.762m \\ \omega=126rpm \\ so\colon \\ v=\omega\cdot r \\ v=126\cdot0.762 \\ v\approx(10.1m)/(s) \end{gathered}`

therefore:

`v\approx(33.14ft)/(s)`