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| | | Wilber Berryhill is the name his parents gave him and he completely digs that name. What me and my family love is performing ballet but I've been taking on new issues recently. He works as a bookkeeper. My spouse and I reside in Kentucky.<br><br>Feel free to visit my web blog ... clairvoyant psychic; [http://www.perfecteyes.com/users/PB63 www.perfecteyes.com], |
| {{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> , | |
| 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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Wilber Berryhill is the name his parents gave him and he completely digs that name. What me and my family love is performing ballet but I've been taking on new issues recently. He works as a bookkeeper. My spouse and I reside in Kentucky.
Feel free to visit my web blog ... clairvoyant psychic; www.perfecteyes.com,