Each of the space shuttle's main engines is fed liquid hydrogen by a high-pressure pump. Turbine blades inside the pump rotate at 595 rev/s. A point on one of the blades traces out a circle with a radius of 0.02 m as the blade rotates.

Question

(a) What is the magnitude of the centripetal acceleration that the blade must sustain at this point?
1 m/s2

(b) Express this acceleration as a multiple of g = 9.80m/s2.

Answer 1

Centripetal acceleration is given by

a = v^2/r = omega^2*r

where a is the centripetal acceleration, v is the speed, r is the radius, and omega is the angular speed in rad/s

Convert rev/s to radians per second
595 rev/s * (2*pi radians/rev) = ____ = omega

a = omega^2 * 0.02 m

b). Divide the centripetal acceleration by g to express it as a multiple of g.