Editing Equations of motion (section)

===Kinematic quantities===
[[File:Kinematics.svg|thumb|300px|Kinematic quantities of a classical particle of mass {{math|''m''}}: position {{math|'''r'''}}, velocity {{math|'''v'''}}, acceleration {{math|'''a'''}}.]]

From the [[instantaneous]] position {{math|'''r''' {{=}} '''r'''(''t'')}}, instantaneous meaning at an instant value of time {{math|''t''}}, the instantaneous velocity {{math|'''v''' {{=}} '''v'''(''t'')}} and acceleration {{math|'''a''' {{=}} '''a'''(''t'')}} have the general, coordinate-independent definitions;<ref name="Relativity">{{cite book | last = Forshaw | first = J. R. | url = https://www.worldcat.org/oclc/291193458 | title = Dynamics and Relativity | date = 2009 | publisher = John Wiley & Sons | author2 = A. Gavin Smith | isbn = 978-0-470-01460-8 | location = Chichester, UK | oclc = 291193458}}</ref>

<math display="block"> \mathbf{v} = \frac{d \mathbf{r}}{d t} \,, \quad \mathbf{a} = \frac{d \mathbf{v}}{d t} = \frac{d^2 \mathbf{r}}{d t^2} </math>

Notice that velocity always points in the direction of motion, in other words for a curved path it is the [[tangent vector]]. Loosely speaking, first order derivatives are related to tangents of curves. Still for curved paths, the acceleration is directed towards the [[center of curvature]] of the path. Again, loosely speaking, second order derivatives are related to curvature.

The rotational analogues are the "angular vector" (angle the particle rotates about some axis) {{math|'''θ''' {{=}} '''θ'''(''t'')}}, angular velocity {{math|'''ω''' {{=}} '''ω'''(''t'')}}, and angular acceleration {{math|'''α''' {{=}} '''α'''(''t'')}}:

<math display="block" qid=Q107617>\boldsymbol{\theta} = \theta \hat{\mathbf{n}} \,,\quad  \boldsymbol{\omega} = \frac{d \boldsymbol{\theta}}{d t} \,, \quad \boldsymbol{\alpha}= \frac{d \boldsymbol{\omega}}{d t} \,,</math>

where {{math|'''n̂'''}} is a [[unit vector]] in the direction of the axis of rotation, and {{math|''θ''}} is the angle the object turns through about the axis.

The following relation holds for a point-like particle, orbiting about some axis with angular velocity {{math|'''ω'''}}:<ref>{{cite book| title=Vector Analysis|edition=2nd|author1=M.R. Spiegel |author2=S. Lipschutz |author3=D. Spellman |series=Schaum's Outlines| page=33| publisher=McGraw Hill|year=2009|isbn=978-0-07-161545-7}}</ref>

<math display="block" qid=Q11465> \mathbf{v} = \boldsymbol{\omega}\times \mathbf{r} </math>

where {{math|'''r'''}} is the position vector of the particle (radial from the rotation axis) and {{math|'''v'''}} the tangential velocity of the particle. For a rotating continuum [[rigid body]], these relations hold for each point in the rigid body.