The period of the enclosed cylinder is approximately 115.866 seconds.
The rotating enclosed cylinder is rotating at constant angular speed ([tex]\omega[/tex]), in radians per second, which means that experiments a constant radial angular acceleration ([tex]\alpha[/tex]), in radians per square second. Then, we derive an expression for the period of the cylinder, this is, the time needed by the cylinder to make one revolution:
[tex]g = \omega^{2}\cdot R[/tex] (1)
Where:
[tex]g = \frac{4\pi^{2}\cdot R}{T^{2}}[/tex]
[tex]T = 2\pi\cdot \sqrt{\frac{R}{g} }[/tex] (2)
Where [tex]T[/tex] is the period, in seconds.
If we know that [tex]R = 3335\,m[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], then the period of the enclosed cylinder is:
[tex]T = 2\pi\cdot \sqrt{\frac{3335\,m}{9.807\,\frac{m}{s^{2}} } }[/tex]
[tex]T \approx 115.866\,s\,(1.931\,min)[/tex]
The period of the enclosed cylinder is approximately 115.866 seconds.
We kindly invite to check this question on circular motion: https://brainly.com/question/2285236
