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 29.9 m/s2 with a beam of length 5.33 m , what rotation frequency is required

Answer 1

Rotation frequency is 0.377 hertz.

Step-by-step explanation:

After a careful reading of statement, we need to apply the concept of radial acceleration due to uniform circular motion, whose formula is:

`a_(r) = \omega^(2)\cdot L` (Eq. 1)

Where:

`a_(r)` - Radial acceleration, measured in meters per square second.

`\omega` - Angular velocity, measured in radians per second.

`L` - Length of the beam, measured in meters.

Now we clear the angular velocity within:

`\omega = \sqrt{(a_(r))/(L) }`

If
`a_(r) = 29.9\,(m)/(s^(2))` and
`L = 5.33\,m`, the angular velocity is:

`\omega = \sqrt{(29.9\,(m)/(s^(2)) )/(5.33\,m) }`

`\omega \approx 2.368\,(rad)/(s)`

The frequency is the number of revolutions done by device per second and can be found by using this expression:

`f = (\omega)/(2\pi)` (Eq. 2)

Where
`f` is the frequency, measured in hertz.

If we know that
`\omega \approx 2.368\,(rad)/(s)`, then rotation frequency is:

`f = (2.368\,(rad)/(s) )/(2\pi)`

`f = 0.377\,hz`

Rotation frequency is 0.377 hertz.