So far in this text, rotations were explored for a rotation about an axis through a given finite angle. In that setting, there is no continuous motion. This chapter examines the case of a continuous rotation about an axis, using angular velocity to measure the rate at which the rotation occurs. Combining angular velocitiesAngular velocity in three dimensions is achieved with simple vector addition and does not involve the more complex operations encountered for combining rotations through fixed angles. Nevertheless, the results of early chapters find use when solving real world problems using kinematic differential equations, examples of which are presented. Kinematics describes motion using quantities that depend on position as a function of time. When an object’s position changes through continuous rotation, the results of previous chapters are used in deriving kinematic differential equations to describe the resulting motion. Rotations within a moving frame are analysed, and examples are provided to illustrate the resulting transport theorem.