# Can a non-inertial frame be viewed as an inertial frame?

Let's consider a non-inertial frame with an acceleration of $$a$$ relative to an inertial frame, if $$a$$ is really small and we don't need extreme accuracy, can we ignore this acceleration and treat this non-inertial frame as an inertial frame because the acceleration is very small?

In other words, a table is fixed to a accelerating car where $$a$$ is really small, I put a ball on this table, is it reasonable to assume that this ball will not move significantly and I can apply Newton's Law to this ball?

• Writing $a\ll 1$ doesn't make sense, because $a$ has units of acceleration, so you can't compare it with a unitless number. Commented Jul 24 at 11:02
• Presumably the "inertial system" you are thinking about is fixed to earth? Commented Jul 24 at 11:20
• Yes, the Earth's surface for example experiences a small centripetal acceleration due to the rotation which is often ignored on tabletop experiments. Commented Jul 24 at 13:31