stylistic:style_transfer, structural:reformatting
Formula

In Newtonian mechanics, the equation of motion for an object in an inertial reference frame is:

where F {\displaystyle {\boldsymbol {F}}} is the vector sum of the physical forces acting on the object, m {\displaystyle m} is the mass of the object, and a {\displaystyle {\boldsymbol {a}}} is the acceleration of the object relative to the inertial reference frame.

Transforming this equation to a reference frame rotating about a fixed axis through the origin with angular velocity ω {\displaystyle {\boldsymbol {\omega }}} having variable rotation rate, the equation takes the form:

where the prime (') variables denote coordinates of the rotating reference frame (not a derivative) and:

The fictitious forces as they are perceived in the rotating frame act as additional forces that contribute to the apparent acceleration just like the real external forces. The fictitious force terms of the equation are, reading from left to right:

As seen in these formulas the Euler and centrifugal forces depend on the position vector r ′ {\displaystyle {\boldsymbol {r'}}} of the object, while the Coriolis force depends on the object's velocity v ′ {\displaystyle {\boldsymbol {v'}}} as measured in the rotating reference frame. As expected, for a non-rotating inertial frame of reference (ω = 0) {\displaystyle ({\boldsymbol {\omega }}=0)} the Coriolis force and all other fictitious forces disappear.