Period and Frequency in Uniform Circular Motion Practice Problems

As humanity ventures into the vastness of space, scientists have proposed the idea of creating artificial gravity on space stations by means of rotation. To test this idea, a team of engineers has designed a massive cylindrical space station with a diameter of 1200 m that rotates about its axis. Determine, what period rotation will provide a gravitational force equivalent to Earth's gravity. 

Astronauts in space are apparently weightless. Weightlessness has many challenges because objects float in space. Objects cannot be placed down and movements are difficult. You decide to introduce artificial gravity in space from spinning. To do so, you attach a ring to the International Space Station and set it to spin about its center. How many revolutions per minute must the ISS (with a 109 m diameter ring attached to it) make about its center to produce artificial gravity equal to Earth's gravity at the surface of the ring?

Gravity has very similar effects to acceleration. However, large accelerations are not so nice to human beings. Scientists have been conducting research on the effects of large accelerations on human beings. Suppose a person with a height of 1.72 m is centrifuged to a maximum acceleration of 9g using a horizontal arm that is 7.50 m long. Assuming the head of the person is positioned at the outermost end of the centrifuge arm, calculate the required rev/min to generate an acceleration of 9g.

Imagine an electron (mass m = 9.1 × 10^-31 kg) revolving around the nucleus of a helium atom, held in orbit by the electric force between them. At a distance of 0.5 × 10^-10 m, this electron experiences an electric force of 1.84 × 10^-7 N. Determine the number of revolutions per second that this electron makes around the nucleus.

An innovative planetary ring system is designed to encircle Mars to create a habitat that simulates Earth-like gravity conditions through its rotation. This system is placed at $2.00\times 10^5\ km$ from the center of Mars. Given that Mars has a mass of $6.42\times 10^{23}\ kg$, calculate the ring system's rotation period, T, in hours. (Let $G=6.67\times 10^{-11}\frac{N\ m^2}{kg^2}$)

What is the frequency of revolution for a small meteoroid in a circular orbit around the Sun with a radius of 1.5 astronomical units (AU)? (Assuming the meteoroid moves in a circular path around the Sun.)