Rotational Motion Homework: Diameters, Revs & Speed of Rotors

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SUMMARY

The discussion focuses on calculating the tip speeds of the main rotor and tail rotor of a single-engine helicopter with diameters of 7.63 m and 0.99 m, and rotational speeds of 459 rev/min and 4132 rev/min, respectively. The correct application of the formula V=Rω is emphasized, where V is the linear speed, R is the radius, and ω is the angular velocity in radians per second. The calculated speeds are 29.18 m/s for the main rotor and 34.10 m/s for the tail rotor, highlighting the importance of understanding the relationship between linear and angular motion.

PREREQUISITES
  • Understanding of rotational motion concepts
  • Familiarity with the formula V=Rω
  • Knowledge of converting rotational speed from rev/min to radians/sec
  • Basic geometry of circles, specifically circumference calculations
NEXT STEPS
  • Learn how to convert rotational speed from rev/min to radians/sec
  • Study the relationship between linear speed and angular frequency in rotational systems
  • Explore the concept of circumference and its application in rotational motion
  • Investigate the effects of rotor diameter on helicopter performance
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Students studying physics, particularly those focusing on rotational dynamics, as well as engineers and mechanics involved in rotorcraft design and performance analysis.

mandy9008
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Homework Statement


The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.63 m and 0.99 m, respectively. The respective rotational speeds are 459 rev/min and 4132 rev/min. Calculate the speeds of the tips of both rotors.


Homework Equations


V=Rω


The Attempt at a Solution


V=(3.815m)(7.65 rev/s)
V=29.18 m/s

V=(.495m)(68.89 rev/s)
V=34.10 m/s
 
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Hello mandy9008,

mandy9008 said:

Homework Equations


V=Rω

The Attempt at a Solution


V=(3.815m)(7.65 rev/s)
V=29.18 m/s

V=(.495m)(68.89 rev/s)
V=34.10 m/s

Not quite. Your relevant equation is good, but your application of it is missing a little something. Here are a few clues:

What is the circumference of a circle in relationship to its radius?

Following the same idea, if something travels around a circle once in a given amount of time, what total distance does it traverse? And at what speed?

Which is really the same question phrased differently, what is the relationship between the angular frequency ω (in radians/sec), and the rotational frequency f (in rotations/sec)?
 

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