physics: rotational motion?
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. Compare these speeds with the speed of sound, 343 m/s.
- 1 decade agoFavorite Answer
so, the first thing you want to do is turn those diameters into radii by dividing by 2
r(main rotor [MR]) = 3.815 m r(tail rotor [TR])= .495 m
now, convert rev/min of each into rad/sec. this is tricky, but this is what you do is multiply
1min/60secs to cancel the minutes
rot(MR) = 7.65 rev/sec rot(TR) = 68.87 rev/sec
next, you convert revs to radians by multiplying 2*Pii
angular speed of MR= 48.1rad/sec, TR= 432.7 rad/sec
finally, you multiply times their respective radii and you come up with
velocity of rotor tips (r*MR) = 183.37 m/s, (r*TR)= 214.19 m/s
Then compare it to 343m/sSource(s): mechatronic engineer