beaker partially filled with water, rotating with angular velocity w about its axis. equation and derivation of parabolic water surface formed. to be done using slope method.

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Derive equation for parabolic water surface formed in a rotating beaker partially filled with water using slope method.

Assume the beaker is rotating with angular velocity w about its axis
Use the slope method to derive the equation for the parabolic water surface formed
The equation is y = (1/2) * (w^2/g) * x^2, where y is the height of the water surface and x is the distance from the axis of rotation
This equation is a result of balancing the centrifugal force and the gravitational force acting on the water molecules
The slope of the water surface at any point is given by dy/dx = (w^2/g) * x, which is a linear function of x

beaker partially filled with water, rotating with angular velocity w about its axis. equation and derivation of parabolic water surface formed. to be done using slope method.

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