#### Answer

The minimum angular velocity is 29.9 rpm

#### Work Step by Step

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.