Our muscles atrophy when there is no gravitational force. On long space flights this is a problem, which is why astronauts exercise. On very long space flights it might be advisable to simulate gravity. Your space ship is a long cylinder of radius \(100~\mbox{m}\) that spins about its axis. What angular velocity **in rad/s** for the spin is needed so that the force felt by a person standing on the rim of the cylinder matches the force of gravity felt on Earth?

**Details and assumptions**

- The acceleration of gravity on earth is \(-9.8~\mbox{m/s}^2\).

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