Can anyone Please help me with this problem? I'm trying to use this formula (velocity = radius * angular velocity), but somehow it's not right Thank You.

 

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 4150 rev/min. Calculate the speeds of the tips of both rotors.

 

main rotor?

tail rotor?

 

Compare these speeds with the speed of sound, 343 m/s.

What are your solutions and what is wrong with them ?

velocity = radius * angular velocity

 

v1=3.8m*450rev/min= 1710/60 = 28.5m/s

v2=0.51m*4150rev/min=2116.5/60 = 35.3m/s

 

Comparison with the speed of sound:

 

vmain rotor / vsound = 28.5m/s/343 m/s= 0.083

vtail rotor / vsound = 35.3m/s/343 m/s= 0.103

 

i really don't know what i am doing wrong...

The angular velocity does not equal the frequency (the rev/min). Think of it: If something goes in a circle at 1 rev/sec, then the magnitude of the velocity equals one circumference per second, not one radius per second.

i got it. Thank You!

Disappointing. If only they went a bit faster!