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A helicopter's main rotor has blades that are $2.75$ meters long. If it rotates at $400$ rev/min, how fast is the tip of one of the blades moving in m/s?

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The velocity is a vector quantity given by $ \vec{v} = r \vec{\omega} $ in tangential direction.

Therefore, $ \vec{v} = 2.75 * 400 $ m/min $ = \frac{1100}{60} $ m/s $ = 18.33 $ m/s.

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For clarity assume the helicopter is not moving.

Then the rotor tip travels in a circle. The circumference of that circle is $\pi$ times the diameter, that is, $2.75\pi$ metres. Thus in $1$ minute the rotor tip travels through $(2.75\pi)(400)$ metres.

If we want the speed in metres per second, divide by $60$.

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Are helicopter blades measured hub-to-tip, or tip-to-tip? – DJohnM Mar 21 '13 at 2:57
I believe that for airplane blades, it is tip to tip. Don't know whether the same applies to helicopters. Assumed that it did. – André Nicolas Mar 21 '13 at 3:04

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