Question

1. A pail of water will be swung with a vertical radius of 1.0 m. What will be the minimum speed so that the water inside the pail will not splash out the pail?

Answer 1

The water inside the pail will not splash out the pail when the centripetal acceleration equals the acceleration due to gravity:

$$a_c=g,\\\space\\ \frac{v^2}{R}=g,\\\space\\ v=\sqrt{gR}=3.1\text{ m/s}.$$