Angular acceleration

DefinitionEdit

Angular acceleration is a vector whose magnitude is defined as the change in angular velocity in unit time.

It is in   in SI unit.

FormulaEdit

Analogous to translational acceleration,  , angular acceleration has the defining formula:

 

in which   represents an instantaneous change in angular velocity,which takes place in  , a short flitting time.


Equivalently, think about the limiting case:  

Relationship with Constant TorqueEdit

The angular acceleration of an fixed-axis-object is proportional to the net torque applied.

 

in which   is the Moment of Inertia of the object.

Angular KinematicsEdit

When an rotation has constant angular acceleration  , the angle displacement   covered in a given time   is given by an equation that is strikingly similar to the equation for displacement under constant acceleration.

 

in which   is the angular velocity at the beginning of the time period  


 

in which case the angular velocity at the beginning   is "zero"


 

in which   is the angular velocity at the end of the time period