Question

A single-engine helicopter has two rotors; a main rotor and a tail rotor. The main rotor has a diameter of 14.8 m and rotates at the rate of 420 rev/min while the tail rotor with a diameter of 1.76 m rotates at 3925 rev/min. What are the speeds, in m/s, of the tips of each rotor?

Answer 1

The speed of the tip of the main rotor is 325.73 m/s, and the speed of the tip of the tail rotor is 363.16 m/s.

Step-by-step explanation:

The speed of the tip of a rotor can be calculated by multiplying the radius of the rotor by its angular velocity. Let's calculate the speeds of the main rotor and tail rotor.

For the main rotor, the radius is half the diameter, so r = 14.8 m / 2 = 7.4 m. The angular velocity is given as 420 rev/min. We need to convert this to radians per second by multiplying by 2π/60, which gives us 43.98 rad/s. Therefore, the speed of the main rotor's tip is 7.4 m * 43.98 rad/s = 325.73 m/s.

For the tail rotor, the radius is half the diameter, so r = 1.76 m / 2 = 0.88 m. The angular velocity is given as 3925 rev/min. Converting this to radians per second gives us 411.56 rad/s. Therefore, the speed of the tail rotor's tip is 0.88 m * 411.56 rad/s = 363.16 m/s.