The forward airspeed of an airplane is 75.0 m/s, and an airplane propeller turns

Question

1. The forward airspeed of an airplane is 75.0 m/s, and an airplane propeller turns at 2400 rpm. (See the right figure.) The speed of the tips of the propeller blades through the air must not exceed 270 m/s. (This is about 80% of the speed of sound in air. With the speed of the propeller tips greater, they would produce a lot of noise.) (12 points)
   1. Convert the angular velocity into rad/s.
   2. What is the maximum possible propeller radius?
   3. With this radius, what is the acceleration of the propeller tip, both radial and tangential components?

Explanation / Answer

1) W = 2400 = (2400*2*3.14)/(60) = 251.2 rad/s

2) V = R*W========> R = V/W = 270/251.2= 1.07 m

3) a_r = V^2/R = 270^2/1.07 = 68130.84 m/s^2

a_t = 0

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