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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.60 m and 1.02 m, respectively. The respective rotational speeds are 450 rev/min and 4 138 rev/min. Calculate the speeds of the tips of both rotors. Compare these speeds with the speed of sound, 343 m/s.

To determine
The speeds of the tips of both rotors and to compare with the speed of light.

Explanation

Given info: The diameter of the main rotor is 7.60m and the diameter of the tail rotor is 1.02m . The rotational speed of main rotor is 450revmin-1 . The rotational speed of the tail rotor is 4138revmin-1 . The speed of the sound is 343ms-1 .

Explanation:

The speeds of rotors is given by,

v=rω

  • r is the radius of the rotor
  • ω is the angular speed of the rotor

In term of the diameter of the rotors,

v=(d2)ω

  • d is the diameter of the rotor

For the main rotor substitute 7.60m for d and 450revmin-1 for ω to determine the speed of the rotor,

v=(7.60m2)(450revmin-1)=(7.60m2)(450revmin-1)(2πradrev-1)(60smin-1)=179ms-1

The ratio of speed of main rotor and speed of sound is,

vrvs=179ms-1343ms-1=0

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