Basic Rotational Quantities

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Angular Velocity

Index Basic rotational quantities  

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Description of RotationRotation is described in terms of angular displacement, time, angular velocity, and angular acceleration. Angular velocity is the rate of change of angular displacement and angular acceleration is the rate of change of angular velocity. The averages of velocity and acceleration are defined by the relationships:
where the Greek letter delta indicates the change in the quantity following it.
You might want to try a numerical exploration of these equations and see them stated in words. 
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Rotation EquationsThese rotation equations apply only in the case of constant angular acceleration. It is assumed that the angle is zero at t=0 and that the motion is being examined at time t. *These quantities are assumed to be given unless they are specifically clicked on for calculation. You can probably do all this calculation more quickly with your calculator, but you might find it amusing to click around and see the relationships between the rotational quantities. It's like a game to see if you can set up a consistent set of parameters. Associated with each active text is a Javascript calculation routine.

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Comments on Rotation CalculationIn the example calculation in the section Rotation Equations above, some assumptions were made about the calculation order. The rotation equations represent a complete set of equations for constant angular acceleration rotations, but in certain types of problems, intermediate results must be calculated before proceeding to the final calculation. In the example calculation, you may have to do intermediate calculations, e.g., to establish the final angular velocity, in order to set up the problem you wish to solve, just as if you were working the problem with calculator and paper. In the example calculation, the time, initial angular velocity, and angular displacement were considered given (primary) unless they were being calculated (e.g., in calculating α). If θ is being calculated, then ω is assumed given, so it must be calculated first if you want to specify α. If initial angular velocity is being calculated, then ω is presumed given. If time is being calculated then α is presumed given. These presumptions are included in the Javascript routines. 
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