Tip speeds of helicopter rotors with different diameters and rotation rates

[mandy9008]

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

 

[collinsmark]

Hello mandy9008,

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)?