Question

Helicopter blades withstand tremendous stresses. In addition to supporting the weight of a helicopter, they are spun at rapid rates and experience large centripetal accelerations, especially at the tip. Calculate the centripetal acceleration at the tip of a 4.20 m long helicopter blade that rotates at 270 rev/min.

Compare the linear speed of the tip with the speed of sound (taken to be 340 m/s), i.e., calculate the ratio of the linear speed over speed of sound.

Answer 1

a.)
(Centripetal Acceleration) = (radius)*(angular velocity)^2
325 rev/min = 34.0339204 radians/second
(Centripetal Acceleration) = (4.00 m)*(34.0339204 radians/second)^2
(Centripetal Acceleration) = 4 633.23095 meters/second^2

b.)
(tangential velocity) = sqrt((centripetal acceleration)*(radius))
just plug them in and get a velocity, then divide that by 340 m/s to get your percentage of the speed of sound, so if you get for example 680, that would be twice the speed of sound or Mach 2