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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?

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Answer:

0.28899 m

Explanation:

v = Velocity = 69 m/s

[tex]\omega[/tex] = Angular velocity = [tex]39\times 2\pi\ rad/s[/tex]

r = Radius of the motion

In rotational motion velocity is given by

[tex]v=r\omega[/tex]

[tex]\\\Rightarrow r=\dfrac{v}{\omega}[/tex]

[tex]\\\Rightarrow r=\dfrac{69}{38\times 2\pi}[/tex]

[tex]\\\Rightarrow r=0.28899\ m[/tex]

The length of the rotation string is 0.28899 m

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