Common approximations |
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The so called laws of physics and the equations of theoretical physics apply exactly in a simplified world. Strings are light (have no weight), strings are inextensible (will not stretch) and bodies are rigid (will not deform). Friction forces are independent of velocity. Pulleys have no moment of inertia. Orbits are circular and not affected by other planets. The list is literally endless. Physics proceeds by writing down equations that apply in these simplified situations and then modifying them slightly to take account of the most important minor effects (perturbations). In all of this, there are a few very useful mathematical approximations. 1 For small angles ... sinq = tanq = q in radians. 2 Neglect terms in x2 and above when x is small. |
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3 A small circular arc and a parabola are almost the same shape. |