en>Unionhawk: Undid good-faith edit by 77.101.129.132 (talk) - "formulas" is also correct, and more common than "formulae"

2014-01-25T20:11:37Z

Undid good-faith edit by 77.101.129.132 (talk) - "formulas" is also correct, and more common than "formulae"

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{{unreferenced|date=October 2012}}

In [[physics]], '''Rotatum''' is the derivative of [[torque]] with respect to [[time]]. Expressed as an equation, rotatum '''Ρ''' is:

:<math>\vec P = \frac{d \vec \tau}{dt}</math>

where '''τ''' is torque and <math>\frac{\mathrm{d}}{\mathrm{d}t}</math> is the derivative with respect to time <math>t</math>.

The term ''rotatum'' is not universally recognized but is commonly used. this word derived from [[Latin]] word ''rotātus'' meaning to rotate. {{Citation needed|date=April 2008}} The units of rotatum are force times distance per time, or equivalently, mass times length squared per time cubed; in the [[SI base units|SI unit system]] this is [[kilogram]] [[metre]] squared per [[second]] cubed (kg·m2/s3), or [[Newton (unit)|Newtons]] times meter per second (N·m2/s).

==Relation to other physical quantities==

[[Newton's second law]] for angular motion says that:

:<math>\mathbf{\tau}=\frac{\mathrm{d}\mathbf{L}}{\mathrm{d}t}</math>

where '''L''' is [[angular momentum]], so if we combine the above two equations:

:<math>\mathbf{\Rho}=\frac{\mathrm{d}\mathbf{\tau}}{\mathrm{d}t}=\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{\mathrm{d}\mathbf{L}}{\mathrm{d}t}\right)=\frac{\mathrm{d}^2\mathbf{L}}{\mathrm{d}t^2}=\frac{\mathrm{d}^2(I\cdot\mathbf{\omega})}{\mathrm{d}t^2}</math>

where <math>I</math> is [[moment of Inertia]] and <math>\omega</math> is [[angular velocity]]. If the moment of inertia isn't changing over time (i.e. it's constant), then:

:<math>\mathbf{\Rho}=I\frac{\mathrm{d}^2\omega}{\mathrm{d}t^2}</math>

which can also be written as:

:<math>\mathbf{\Rho}=I\zeta</math>

where '''ς''' is [[Angular jerk]].

==See also==
*[[Turn (angular quantity)|Turn]]
*[[Angular Jerk]]

[[Category:Dynamics]]

{{physics-stub}}

Formulas for constant acceleration - Revision history

en>Unionhawk: Undid good-faith edit by 77.101.129.132 (talk) - "formulas" is also correct, and more common than "formulae"