Question

A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 38 rev/s, and its tip has a tangential speed of 69 m/s. What is the length of the rotating string?

Answer 1

Answer:

0.28899 m

Explanation:

v = Velocity = 69 m/s

$\omega$ = Angular velocity = $39\times 2\pi\ rad/s$

r = Radius of the motion

In rotational motion velocity is given by

$v=r\omega$

$\\\Rightarrow r=\dfrac{v}{\omega}$

$\\\Rightarrow r=\dfrac{69}{38\times 2\pi}$

$\\\Rightarrow r=0.28899\ m$

The length of the rotation string is 0.28899 m