Friday, June 15, 2018

homework and exercises - Proof of Archimedes Principle


Say I have an arbitrary body $\Omega$ and surface $\partial \Omega$ submerged in a hydrostatic fluid of density $\rho$ under the influence of gravity. How does one show Archimedes Principle? i.e.


$$\int_{\partial \Omega}(P_0 + \rho g h)d\vec{S}=\text{vol}(\Omega)\rho g\vec{e_2}.$$





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classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...