# IPhO2001-EXP - IPhO2001-experimental competition...

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IPhO2001-experimental competition 2 ROTATING LIQUID This experiment consists of three basic parts: 1. investigation of the profile of the rotating liquid’s surface and the determination of the acceleration due to gravity, 2. investigation of the rotating liquid as an optical system, 3. determination of the refractive index of the liquid. When a cylindrical container filled with a liquid rotates about the vertical axis passing through its center with a uniform angular velocity ϖ , the liquid’s surface becomes parabolic (see Figure 1). At equilibrium, the tangent to the surface at the point P( x, y ) makes an angle θ with the horizontal such that R x for g x tan ϖ = 2 θ (1) where R is the radius of the container and g is the acceleration due to gravity. It can further be shown that for ϖ < ϖ max (where ϖ max is the angular speed at which the center of the rotating liquid touches the bottom of the container) at x=x 0 = 2 R , y(x 0 )=h 0 (2) that is; the height of the rotating liquid is the same as if it were not rotating.
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