finding magnitude given tangential acceleration

Question

A propeller blade has a length of 2.42 m and, starting from rest, the tip of the blade has a tangential acceleration of 2.73 m/s2.

What is the magnitude of the total acceleration of the blade, in m/s2, 0.97 s after the blade starts rotating?

Answer 1

The Magnitude of the Total Acceleration = Sqrt (tangential acceleration squared PLUS centripetal acceleration squared). They are perpendicular vectors.

The centripetal acceleration is tangential velocity squared divided by radius of circular motion.

v(tangential) = a(tangential) x (time) = 2.73 x 0.97 = 2.648 metes/sec

Assume the blade is 2x times the radius. The blade length is the Diameter of blade rotation.

So A(centripetal) = (2.648)squared / (2.42 / 2) = 5.8 m / sec squared

Thus Total acceleration = Sqrt ( 2.73 squared PLUS 5.8 squared ) = Sqrt 41.04

Total acceleration = 6.4 meters per second squared