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