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)
Convert the angular velocity into rad/s.
What is the maximum possible propeller radius?
With this radius, what is the acceleration of the propeller tip, both radial and tangential components?