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| {{infobox unit
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| | name = Radians per second squared
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| | standard = [[SI derived unit]]
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| | quantity = Angular acceleration
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| | symbol = rad/s{{sup|2}}
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| | symbol2 = rad⋅s<sup>−2</sup>
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| }}
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| {{Classical mechanics|cTopic=Fundamental concepts}}
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| '''Angular acceleration''' is the rate of change of [[angular velocity]]. In [[SI]] units, it is measured in [[radian]]s per [[second]] squared (rad/s{{sup|2}}), and is usually denoted by the Greek letter [[alpha (letter)|alpha]] (''α'').<ref> http://theory.uwinnipeg.ca/physics/circ/node3.html </ref> | |
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| == Mathematical definition ==
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| The angular acceleration can be defined as either:
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| :<math>{\alpha} = \frac{{d\omega}}{dt} = \frac{d^2{\theta}}{dt^2}</math> , or <br>
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| :<math>{\alpha} = \frac{a_T}{r}</math> ,
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| where <math>{\omega}</math> is the [[angular velocity]], <math>a_T</math> is the linear [[tangential acceleration]], and <math>r</math>, (usually defined as the radius of the circular path of which a point moving along), is the distance from the origin of the [[coordinate system]] that defines <math>\theta</math> and <math>\omega</math> to the point of interest.
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| == Equations of motion ==
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| For two-dimensional [[rotation|rotational motion]] (constant <math>\hat L</math>), [[Newton's laws of motion#Newton's second law|Newton's second law]] can be adapted to describe the relation between [[torque]] and angular acceleration:
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| :<math>{\tau} = I\ {\alpha}</math> ,
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| where <math>{\tau}</math> is the total torque exerted on the body, and <math>I</math> is the [[Moment_of_inertia|mass moment of inertia]] of the body.
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| ===Constant acceleration===
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| For all constant values of the torque, <math>{\tau}</math>, of an object, the angular acceleration will also be constant. For this special case of constant angular acceleration, the above equation will produce a definitive, constant value for the angular acceleration:
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| :<math>{\alpha} = \frac{\tau}{I}.</math>
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| ===Non-constant acceleration===
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| For any non-constant torque, the angular acceleration of an object will change with time. The equation becomes a differential equation instead of a constant value. This [[differential equation]] is known as the equation of motion of the system and can completely describe the motion of the object. It is also the best way to calculate the angular velocity.
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| == See also ==
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| * [[Angular momentum]]
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| * [[Angular speed]]
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| * [[Angular velocity]]
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| * [[Rotation]]
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| * [[Spin (physics)|Spin]]
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| ==References==
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| {{reflist}}
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| [[Category:Physical quantities]]
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| [[Category:Acceleration]]
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