The angular displancment is defined by: For a circular path it follows that the angular velocity is and the angular acceleration is where the acceleration here is the tangential acceleration.
The standard angle of a directed quantity is taken to be counterclockwise from the positive x axis.
Index

centripetal acceleration

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# Angular Velocity

### Vector angular velocity

For an object rotating about an axis, every point on the object on the object has the same angular velocity. The tangential velocity of any point is proportional to its distance from the axis of rotation. Angular velocity has the units rad/s.

Angular velocity is the rate of change of angular displacement and can be described by the relationship

and if v is constant, the angle can be calculated from

Index

Basic rotational quantities

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# Description of Rotation

Rotation 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.

 A bar above any quantity indicates the average value of that quantity. If a is constant, equations 1,2, and 3 represent a complete description of the rotation. Equation 4 is obtained by a combination of the others.
Index

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# Rotation Equations

These rotation equations apply only in the case of constant angular acceleration. It is assumed that u=0 at t=0 and that the motion is being examined at time t. angular displacement = average angular velocity x time angular velocity = initial angular velocity + ang. acceleration x time ang. displacement = initial ang. velocity x t + ang. accel. x time
Index

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