Question

The motor on a helicopter turns at an angular speed of 6.2 x 102 revolutions per minute. (a) Express this angular speed in radians per second.

(b) If the rotor has a radius of 3.0 m, what arc length (linear displacement) tip of the blade trace out in 2.0 x 102 s?​

Answer 1

• 64.93 rad/s
• 38.956 km

Step-by-step explanation:

(a)

`\frac{6.2\cdot 10^2\,\text{rev}}{60\,\text{s}}*\frac{2\pi\,\text{rad}}{\text{rev}}=\frac{62\pi\,\text{rad}}{3\,\text{s}}\approx\boxed{64.93\,\text{rad/s}}`

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(b)

`d=r\theta=(3.0\,\text{m})(2.0\cdot 10^2\,\text{s})\left(\frac{62\pi\,\text{rad}}{3\,\text{s}}\right)=124\pi\cdot 10^2\,\text{m}=\boxed{38\,956\,\text{m}}`