# Angular velocity question. Help

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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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 $60$.