The Accelerated Angular Velocity calculator computes the angular acceleration based on an initial angular velocity, a constant acceleration and a duration of acceleration.

INSTRUCTIONS: Choose units and enter the following:

• (ω₀) Initial Angular Velocity
• (α) Constant Angular Acceleration
• (t) Duration of Acceleration

Accelerated Angular Velocity (ω): The calculator returns the angular velocity in radians per second.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The angular velocity,`omega`, describes the speed of rotation and typically, when specified in vector form, also describes the instantaneous orientation of the axis of rotation.  This equation computes the magnitude of the angular velocity, aka angular speed, (`omega`) of a rigid body when the applied moment about a fixed axis is constant.  The angular velocity can be integrated with respect to time, starting at time t = 0.

The inputs to this equation are:

• `omega_0` - initial angular velocity
• `t` - elapsed time after t = 0
• `alpha` - angular acceleration

author: Michael Bartmess

Notes

In physics, the angular velocity is defined as the rate of change of angular displacement and is a vector quantity which specifies the angular speed (rotational speed) of an object and the axis about which the object is rotating.

The angular velocity vector, `vec omega`, would be pointing along the vector orientation of the axis of rotation using the right hand rule for positive and negative rotation direction.  I.e, if the rotation were in the x-y plane as shown in the picture, the velocity vector would be pointing normal to the x-y plane in the positive z direction.

In this equation, velocity is a function of the time over which angular acceleration occurs.