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 48 rev/s, and its tip has a tangential speed of 50 m/s. What is the length of the rotating string?

0.166 m or 16.6 cm

Explanation:

From the question,

v = ωr Equation 1

Where v = tangential speed of the string, ω = Angular speed of the string, r = Length of the rotating string.

make r the subject of the equation

r = v/ω Equation 2

Given: v = 50 m/s, ω = 48 rev/s = 48(2π) rad/s = 48(2×3.14) rad/s = 301.44 rad/s.

Substitute into equation 2

r = 50/301.44

r = 0.166 m or 16.6 cm

Hence the length of the rotating string = 0.166 m or 16.6 cm

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