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 9:30am11:18am 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 corotating 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
~ω
.
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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 Fall '04
 BUNDSCHUH
 mechanics, Mass, Rotation, Angular velocity, inertia tensor, Theoretical Mechanics

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