A single-engine helicopter has two rotors; a main rotor and a tail rotor. The main rotor has a diameter of 14.4 m and rotates at the rate of 450 rev/min while the tail rotor with a diameter of 1.6 m rotates at 4100 rev/min. What are the speeds, in m/s, of the tips of each rotor? main rotor speed m/s tail rotor speed m/s

339.12 m/s, 343.31 m/s

Explanation:

For main rotor

diameter, d = 14.4 m

radius, r = 7.2 m

f = 450 rev/min = 450 / 60 = 7.5 rps

Angular speed, ω = 2 x π x f = 2 x 3.14 x 7.5 = 47.1 rad/s

linear speed, v = r x ω = 7.2 x 47.1 = 339.12 m/s

For tail rotor

diameter, d = 1.6 m

radius, r = 0.8 m

f = 4100 rev/min = 4100 / 60 = 68.33 rps

Angular speed, ω = 2 x π x f = 2 x 3.14 x 68.33 = 429.13 rad/s

linear speed, v = r x ω = 0.8 x 429.13 = 343.31 m/s