A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates ab

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 52 rev/s, and its tip has a tangential speed of 54 m/s. What is the length of the rotating string?

Answer 1

54 m/s / 52 rev/s = 54/52 m/rev
C = 2 pi r
r = 54 / (104 * pi) = 0.165 m (rounded down)

Answer 2

1 rev = 2*pi*r meters
Substitute
52 rev/s * (2*pi*r) m/rev = 54 m/s
Solve
r = 54 / (52*2*pi) = 0.165 m or 16.5 cm.

I hope this helps!