Question

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min.

(a) What is the linear speed of the blade tip, in m/s?

(b) What is the radial acceleration of the blade tip expressed as a multiple of the acceleration?

Answer 1

a) The linear speed in circular motion is given as follows:

$$v = 2\pi fr$$

where $f = 550rev/min = \dfrac{55}{6}rev/min$ is the frequency, and $r=3.4m$ is the radius. Thus, obtain:

$$v = 2\pi\cdot \dfrac{55}{6}\cdot 3.4 \approx 196m/s$$

b) The radial acceleration is given as follows:

$$a = \dfrac{v^2}{r} = \dfrac{196^2}{3.4} \approx 57.6m/s^2$$

Answer. a) 196 m/s, b) 57.6 m/s^2.