Answer:
Rotation frequency is 0.377 hertz.
Explanation:
After a careful reading of statement, we need to apply the concept of radial acceleration due to uniform circular motion, whose formula is:
[tex]a_{r} = \omega^{2}\cdot L[/tex] (Eq. 1)
Where:
[tex]a_{r}[/tex] - Radial acceleration, measured in meters per square second.
[tex]\omega[/tex] - Angular velocity, measured in radians per second.
[tex]L[/tex] - Length of the beam, measured in meters.
Now we clear the angular velocity within:
[tex]\omega = \sqrt{\frac{a_{r}}{L} }[/tex]
If [tex]a_{r} = 29.9\,\frac{m}{s^{2}}[/tex] and [tex]L = 5.33\,m[/tex], the angular velocity is:
[tex]\omega = \sqrt{\frac{29.9\,\frac{m}{s^{2}} }{5.33\,m} }[/tex]
[tex]\omega \approx 2.368\,\frac{rad}{s}[/tex]
The frequency is the number of revolutions done by device per second and can be found by using this expression:
[tex]f = \frac{\omega}{2\pi}[/tex] (Eq. 2)
Where [tex]f[/tex] is the frequency, measured in hertz.
If we know that [tex]\omega \approx 2.368\,\frac{rad}{s}[/tex], then rotation frequency is:
[tex]f = \frac{2.368\,\frac{rad}{s} }{2\pi}[/tex]
[tex]f = 0.377\,hz[/tex]
Rotation frequency is 0.377 hertz.
