# Inertial reference frames and Newton's Laws of Motion

The first law of motion says that it takes force to accelerate something.
The second law of motion says that F=ma.

So now my teacher says that the first law is for inertial reference frames, while the second is for non-inertial reference frames.

This really annoys me because I don't understand how they are related.

I thought that both laws only work in inertial reference frames, or else we'll have to add "fictional" forces" like centrifugal forces, right? Why does the second law apply to non-inertial reference frames?

D H
Staff Emeritus
So now my teacher says that the first law is for inertial reference frames, while the second is for non-inertial reference frames.

I thought that both laws only work in inertial reference frames, or else we'll have to add "fictional" forces" like centrifugal forces, right? Why does the second law apply to non-inertial reference frames?
It's important to look at Newton's laws from the perspective of thinking at Newton's time. Aristotelian physics said that the natural state of some object is being at rest; a moving object required some force to keep it in motion. One of the reasons for the first law (which nowadays seems redundant with the second law) was to explicitly counter this Aristotelian view. The natural state of some object is whatever state in which it happens to be. If it is at rest, it will remain at rest unless a force acts upon it. Moving, it will keep moving at a constant velocity unless a force acts upon it.

The modern view is that the first law defines the context in which Newton's other two laws work: It provides a null test of whether a frame of reference is an inertial frame. Strictly speaking, Newton's second law applies to real forces only and is thus only valid in inertial frames. Newton's second law can be extended to non-inertial frames by means of fictitious forces, but this was developed well after Newton's death. Note well: These fictitious forces are not subject the Newton's third law.

So you're saying that by adding fictitious forces Newton's Second Law also works in non-inertial frames?

D H
Staff Emeritus
Yes. However, that is not the point of Newton's second law. It works quite nicely in inertial frames as well.

The point of Newton's second law is that it is able to predict the behavior of a system of objects. Newton's first law is only of help in the trivial case of no net forces. Newton's second law covers that case plus any other case for which one can somehow express the forces acting on the objects of interest.

This assumes of course that Newton's laws do apply. Newton's laws are not as universal as Newton thought. They don't apply in the realms of the very small (quantum mechanics), very fast (special relativity), very massive (general relativity), or very large (cosmology).