In this section we derive some useful relationships between the angular speed and acceleration of a rotating rigid object and the linear speed and acceleration of a point in the object. To do so, When a rigid object rotates about a fixed axis, as in Figure 30, every particle of the object moves in a circle whose center is the axis of rotation.

Because point P in Figure 30 moves in a circle, the linear velocity vector v is always tangent to the circular path and hence is called tangential velocity.