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

0.28899 m

Step-by-step explanation:

v = Velocity = 69 m/s

`\omega` = Angular velocity =
`39* 2\pi\ rad/s`

r = Radius of the motion

In rotational motion velocity is given by

`v=r\omega`

`\\\Rightarrow r=(v)/(\omega)`

`\\\Rightarrow r=(69)/(38* 2\pi)`

`\\\Rightarrow r=0.28899\ m`

The length of the rotation string is 0.28899 m