bilateral symmetry

Examples of bilateral symmetry in the following topics:

• Key Points: Range, Symmetry, Maximum Height

  • Projectile motion is a form of motion where an object moves in a bilaterally symmetrical, parabolic path.
  • All projectile motion happens in a bilaterally symmetrical path, as long as the point of projection and return occur along the same horizontal surface.
  • Bilateral symmetry means that the motion is symmetrical in the vertical plane.
  • This is also the point where you would draw a vertical line of symmetry.

• Locating the Center of Mass

  • The center of mass of a body with an axis of symmetry and constant density must lie on this axis.
  • In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry.

• The Third Law: Symmetry in Forces

  • If object A exerts a force on object B, because of the law of symmetry, object B will exert a force on object A that is equal to the force acted on it:

• Electric Flux

  • While Gauss' Law holds for all situations, it is only useful for "by hand" calculations when high degrees of symmetry exist in the electric field.
  • Examples include spherical and cylindrical symmetry.

• Inverse Compton Power - Single Scattering

  • Remember that $d^3 x = \gamma d^3 x'$ and that $E = \gamma E'$ (with forward-backward symmetry) so we find that

• The Born-Oppenheimer Approximation

  • For diatomic molecules there is still a rotational symmetry about the line connecting the two nuclei.

• Electric Potential Due to a Point Charge

  • Note the symmetry between electric potential and gravitational potential - both drop off as a function of distance to the first power, while both the electric and gravitational fields drop off as a function of distance to the second power.

• Effects of Time Dilation: The Twin Paradox and the Decay of the Muon

  • Since there is no symmetry, it is not paradoxical if one twin is younger than the other.

• Electron Configurations

  • The molecular orbitals are labelled according to their symmetry, rather than the atomic orbital labels used for atoms and monoatomic ions: hence, the electron configuration of the diatomic oxygen molecule, O2, is 1σg2 1σu2 2σg2 2σu2 1πu4 3σg2 1πg2.

• Rosseland Approximation

  • Because stellar atmospheres (i.e. the effective mean path) are generally thin compared to the size of the star, we can assume that this region has plane parallel symmetry; that is, the properties of the material depend only on the depth from the surface $z$.