In the diagram below there is a thick-walled cylindrical tube. Its height is H 5.0 m, its inner radius is R1 = 1.0 m, its outer radius is R2= 3.0 m and its mass is M = 10.0 kg. The volume density is proportional to the square of the height h measured from the top of the cylinder: p « h?.
In the diagram below there is a thick-walled cylindrical tube. Its height is H 5.0 m, its inner radius is R1 = 1.0 m, its outer radius is R2= 3.0 m and its mass is M = 10.0 kg. The volume density is proportional to the square of the height h measured from the top of the cylinder: p « h?.
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Transcribed Image Text:In the diagram below there is a thick-walled cylindrical tube. Its height is H = 5.0 m, its
inner radius is R1 = 1.0 m, its outer radius is R2 = 3.0 m and its mass is M = 10.0 kg. The
volume density is proportional to the square of the height h measured from the top of the
cylinder: p x h?.
R2
a) Proof that the proportionality constant k (p = kh?) is k = ,
ms
100m
b) Determine the position of the center of mass of this object.
c) Determine I, the moment of inertia of the cylindrical tube around the axle going
through the center of the top (as shown on diagram). You can use lying =mr? (the
rotational inertia of a ring of radius r and mass m rotating around an axis parallel to
it, through its center).
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