Question

A device for acclimating military pilots to the high accelerations they must experience consists of a horizontal beam that rotates horizontally about one end while the pilot is seated at the other end. In order to achieve a radial acceleration of 32.7 m/s2 with a beam of length 5.29 m , what rotation frequency is required

Answer 1

Answer:

The rotation frequency required is 23.78 RPM

Explanation:

Given;

radial acceleration, a = 32.7 m/s²

length of the beam, r = 5.29 m

The linear velocity is calculated as;

$a = \frac{v^2}{r} \\\\v^2 = ar\\\\v = \sqrt{ar}$

where;

v is linear velocity

The angular velocity is calculated as;

$\omega = \frac{v}{r} \\\\Recall, v = \sqrt{ar} \\\\Then, \omega = \frac{\sqrt{ar}}{r}} \\\\ \omega = \frac{\sqrt{32.7 \times5.29}}{5.29}\\\\\omega = 2.49 \ rad/s\\\\Angular \ frequency \ is \ calculated \ as;\\\\\omega = 2\pi f\\\\f = \frac{\omega}{2\pi} \\\\f = \frac{2.49}{2\pi} \\\\f = 0.396 \ rev/s\\\\f = 23.78 \ rev/min$

Therefore, the rotation frequency required is 23.78 RPM