Talk:PlanetPhysics/Acceleration

Original TeX Content from PlanetPhysics Archive

%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: acceleration %%% Primary Category Code: 45.05.+x %%% Filename: Acceleration.tex %%% Version: 1 %%% Owner: pbruin %%% Author(s): pbruin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

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The \emph{acceleration} of an \htmladdnormallink{object}{http://planetphysics.us/encyclopedia/TrivialGroupoid.html} is the time derivative of its \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html}. Like velocity, acceleration can therefore be considered either as a \htmladdnormallink{vector}{http://planetphysics.us/encyclopedia/Vectors.html} quantity or as a \htmladdnormallink{scalar}{http://planetphysics.us/encyclopedia/Vectors.html} quantity. Acceleration is usually denoted by the symbol $a$, by $\dot v$ (the time derivative of the velocity) or by $\ddot x$ (the second time derivative of the \htmladdnormallink{position}{http://planetphysics.us/encyclopedia/Position.html}). We can write the definition of acceleration (in vector form) as follows:

$$ \mathbf{a}(t)\equiv\frac{\mathrm{d}\mathbf{v}(t)}{\mathrm{d}t}. $$

The SI unit of acceleration is $\mathrm{m/s^2}$ (metres per second per second, or metres per second squared). Another unit of acceleration is $g$, defined as $g=9.80665\;\mathrm{m/s^2}$; this is approximately the acceleration due to gravity at the surface of the Earth at a latitude of $45^\circ$.

In addition to acceleration as the time derivative (instantaneous rate of change) of velocity, the \emph{average acceleration}, or the change of velocity $\Delta\mathbf{v}$ over a specified period of time $\Delta\mathbf{t}$, can also be defined: $$ \mathbf{\bar a}\equiv\frac{\Delta\mathbf{v}}{\Delta t}. $$

In \htmladdnormallink{classical mechanics}{http://planetphysics.us/encyclopedia/MathematicalFoundationsOfQuantumTheories.html}, acceleration is caused by forces. If a total force $\mathbf{F}$ acts on an object with constant \htmladdnormallink{mass}{http://planetphysics.us/encyclopedia/Mass.html} $m$, the object undergoes an acceleration $\mathbf{a}$ as described by Newton's second law: $$ \mathbf{F}=m\mathbf{a}. $$ In contrast to velocity, which depends on the observer's \htmladdnormallink{system}{http://planetphysics.us/encyclopedia/SimilarityAndAnalogousSystemsDynamicAdjointnessAndTopologicalEquivalence.html} of reference, acceleration can be called an \emph{absolute} quantity, in the sense that two observers moving with constant velocity with respect to each other perceive the same acceleration.

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