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# set9 - Department of Physics The Ohio State University Prof...

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Department of Physics Prof. R. Bundschuh The Ohio State University Ninth Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: May 31 no class, Jun 9 9:30am-11:18am Fnal exam Due date: Thursday, Jun 3 23. Bucket of water 0+8 points A cylindrical bucket of water is spinning around its symmetry axis with angular velocity ω . We want to calculate the shape of the water surface in this rotating bucket. We assume that the water molecules are at rest in the co-rotating coordinate systems (which in reality is true on average). a) Write down the e±ective force a water particle of mass m on the surface is feeling as a function of the true force, the position ~ r and mass m of the particle and the angular velocity . b) The two true forces acting on a water particle of mass m are the gravitational force and the force ~ F p due to the pressure gradient at the surface. Use the fact that the latter is normal to the surface to calculate the angle θ ( r

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set9 - Department of Physics The Ohio State University Prof...

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