Newton’s laws take their simplest form in inertial frames, which are not accelerating. In a non-inertial frame, objects can appear to accelerate even when no real net force in the inertial frame explains that motion alone.

To use Newton’s laws inside an accelerating frame, introduce fictitious forces such as the inertial force $-m\vec{a}_{\text{frame}}$. These are not interaction forces; they are bookkeeping devices that make $\sum \vec{F} = m\vec{a}$ work in the accelerating frame.

In rotating frames, additional apparent forces arise, including centrifugal and Coriolis effects. These are important in meteorology, rotating machinery, and many Earth-rotation problems.