## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

We can find the minimum angular velocity at the top of the circle. At the minimum angular velocity, the force of gravity provides the centripetal force to keep the water moving in a circle. We can let the radius of rotation be 1.0 meter. $F_c = m~\omega^2 ~r = mg$ $\omega = \sqrt{\frac{g}{r}}$ $\omega = \sqrt{\frac{9.80~m/s^2}{1.0~m}}$ $\omega = 3.13~rad/s$ We can convert the minimum angular velocity to rpm. $\omega = (3.13~rad/s)(\frac{1~rev}{2\pi~rad})(\frac{60~s}{1~min})$ $\omega = 29.9~rpm$ The minimum angular velocity is 29.9 rpm.