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When the expression for acceleration is multiplied by the mass of the particle, the three extra terms on the right-hand side result in [[fictitious force]]s in the rotating reference frame, that is, apparent forces that result from being in a [[non-inertial reference frame]], rather than from any physical interaction between bodies.
Using [[Newton's laws of motion|Newton's second law of motion]] <math>\mathbf{F}=m\mathbf{a},</math> we obtain:<ref name=Arnold/><ref name=Lanczos/><ref name=Taylor/><ref name=Landau>{{cite book |title=Mechanics |author=LD Landau |author2=LM Lifshitz |name-list-style=amp |page= 128 |url=https://books.google.com/books?id=e-xASAehg1sC&pg=PA40 |edition=Third |date=1976 |publisher=Butterworth-Heinemann |isbn=978-0-7506-2896-9}}</ref><ref name=Hand/>
* the [[Coriolis force]] <math display="block">
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