Mathematical definition 
The angular acceleration can be defined as either:
- , or
where is the angular velocity, is the linear tangential acceleration, and , (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 and to the point of interest.
Equations of motion 
where is the total torque exerted on the body, and is the mass moment of inertia of the body.
Constant acceleration 
For all constant values of the torque, , 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:
Non-constant acceleration 
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.