Answer to Question #234806 in Physics for sam

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 is given as follows:

$$v = 2\pi f R$$

where $f = 550rev/min = \dfrac{55}{6}rev/s$ is the frequency of rotation, and $R = 3.4m$ is the distance from the center to the tip. Thus, obtain:

$$v = 2\pi \cdot \dfrac{55}{6}s^{-1}\cdot 3.4m \approx 196m/s$$

b) The radial acceleration is given as follows:

$$a = \dfrac{v^2}{R} = \dfrac{(196m/s)^2}{3.4m} \approx 1.13\times 10^{4}m/s^2$$

Answer. a) $196 m/s$ , b) $1.13\times 10^{4}m/s^2$.