Question

The propeller of a WW2 fighter plane is 2.35 m in diameter

Answer 1

A) 1 rev = 2π rad. Using this ratio, you can find the rad/s: 1160 rev/min x 2π rad/rev x 1 min/60 s = 121.5 rad/s

b) You can find linear speed from angular speed using this equation (note the radius is half the diameter given in the question): v = ωr = 121.5 rad/s x 1.175 m = 142.8 m/s

c) You can find centripetal acceleration using this equation: a = v^2/r = (142.8 m/s)^2 / 1.175 m = 17 355 m/s^2

Answer 2

Angular velocity =

                       (angle turned) / (time)

                   =  (1160 rev/min) x (1 min)/60sec) x (2π radians/rev)

                   =      38-2/3 π radians/sec  =  about  121.5 rad/sec

The length of 1 radian around the circumference is equal to
the radius of the circle.  (That's the definition of the radian.)

Radius of the circle  = 1/2 length of the prop = 1.175 meter

              (121.5 radian/sec) x (1.175 meter) =  142.7 meters/sec

Centripetal acceleration  =  (speed)² / (radius)

                                           =  (142.7 m/s)² / (1.175 m)

                                           = (20,372.7 m²/s²) / (1.175 m)

                                           =      17,338 m/s²

                                        (about 1,770 Gs) ! !