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I am spinning a bucket of water about its vertical axis
Chapter 9, Problem 9.14(choose chapter or problem)
I am spinning a bucket of water about its vertical axis with angular velocity C2. Show that, once the water has settled in equilibrium (relative to the bucket), its surface will be a parabola. (Use cylindrical polar coordinates and remember that the surface is an equipotential under the combined effects of the gravitational and centrifugal forces.)
Questions & Answers
QUESTION:
I am spinning a bucket of water about its vertical axis with angular velocity C2. Show that, once the water has settled in equilibrium (relative to the bucket), its surface will be a parabola. (Use cylindrical polar coordinates and remember that the surface is an equipotential under the combined effects of the gravitational and centrifugal forces.)
ANSWER:Step 1 of 3
The centripetal force is given as,
Here, is the mass of the object, is the angular velocity and is the radius of the object.
The gradient of the potential is given as,
Here, is the potential of the object.