Question

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

a) What is the angular velocity in radians per second if it spins at 1160 rev/min?
b) What is the linear speed (in m/s) of its tip if the plane is stationary on the tarmac?
c) What is the centripetal acceleration of the propeller tip under these conditions? Represent your answer in meters per second squared.
Show work please :)

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) ! !