To calculate the total amount of energy that would be released by the Sun in such a mechanism ( assuming uniform density ), it was approximated to a perfect sphere made up of concentric shells.
42.
Each of the three centroid of the triangle, which is its center of mass if it has uniform density; thus any line through a triangle's centroid and one of its vertices bisects the opposite side.
43.
Thanks to these vector identities, the incompressible Euler equations with constant and uniform density and without external field can be put in the so-called " conservation " ( or Eulerian ) differential form, with vector notation:
44.
:: It's easy now, you have three point masses, you must have learned how to calculate the CofM of a system of point masses before you moved on to having to integrate for a uniform density object.
45.
In fact, the case of incompressible Euler equations with constant and uniform density being analyzed is a toy model featuring only two simplified equations, so it is ideal for didactical purposes even if with limited physical relevancy.
46.
The centroid of a rigid triangular object ( cut out of a thin sheet of uniform density ) is also its center of mass : the object can be balanced on its centroid in a uniform gravitational field.
47.
In a more strict definition, it is the superficial barycenter of the mass distribution produced by treating each continent or island as a region of a thin shell of uniform density and approximating the geoid with a sphere.
48.
The value for Earth is a bit larger than the number given in the article because Earth is not of uniform density; it's about 2.4 * 10 32 talk ) 08 : 50, 22 December 2008 ( UTC)
49.
The tip of the peak is so sharp that a critical exponent characterizing the divergence of the heat capacity can be measured precisely only in zero gravity, to provide a uniform density over a substantial volume of fluid.
50.
This method can be extended ( in theory ) to concave shapes where the centroid lies outside the shape, and to solids ( of uniform density ), but the positions of the plumb lines need to be recorded by means other than drawing.
