The direction and magnitude of the Euler acceleration is given by:

That reactive acceleration is the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration or transverse acceleration.

In classical mechanics, the Euler acceleration (named for Leonhard Euler), also known as azimuthal acceleration or transverse acceleration is an acceleration that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axis.