Inertial reference frames and Newton's Laws of Motion

In summary, the conversation discusses the first and second laws of motion, and the difference between inertial and non-inertial reference frames. The first law states that an object will remain at rest or in motion unless acted upon by a force, while the second law relates force to acceleration. The first law was created to counter the Aristotelian belief that objects require a constant force to maintain motion. The modern view is that the first law defines the context for the other two laws to work, and the second law only applies to real forces in inertial frames. However, it can be extended to non-inertial frames through the use of fictitious forces. The second law is able to predict the behavior of a system of objects, while
  • #1
titaniumpen
45
0
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?
 
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  • #2
titaniumpen said:
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.
 
  • #3
So you're saying that by adding fictitious forces Newton's Second Law also works in non-inertial frames?
 
  • #4
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).
 
  • #5


I understand your frustration and confusion. Let me explain the relationship between inertial reference frames and Newton's Laws of Motion.

An inertial reference frame is a frame of reference in which Newton's Laws of Motion hold true without the need for any additional forces. This means that in an inertial reference frame, an object will remain at rest or continue moving at a constant velocity unless acted upon by an external force. The first law of motion, also known as the law of inertia, states this exact principle.

However, when we move to non-inertial reference frames, such as a rotating frame or an accelerating frame, the laws of motion do not hold true without the addition of "fictional" forces. These forces, like centrifugal force, are not actual physical forces but rather perceived forces due to the frame of reference.

Now, let's look at the second law of motion, F=ma. This law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law applies to both inertial and non-inertial reference frames. In an inertial frame, the acceleration is solely due to the applied force, while in a non-inertial frame, the acceleration is a combination of the applied force and the "fictional" forces.

In summary, the first law of motion only applies to inertial reference frames, while the second law applies to both inertial and non-inertial frames. The second law still holds true even in non-inertial frames, but the addition of "fictional" forces must be taken into account. I hope this helps clarify the relationship between inertial reference frames and Newton's Laws of Motion.
 

1. What is an inertial reference frame?

An inertial reference frame is a coordinate system in which Newton's Laws of Motion hold true. This means that an object in this reference frame will remain at rest or in uniform motion unless acted upon by an external force.

2. How is an inertial reference frame different from a non-inertial reference frame?

A non-inertial reference frame is a coordinate system in which Newton's Laws of Motion do not hold true. This means that an object in this reference frame may appear to accelerate even if no external forces are acting on it.

3. What is the relationship between inertia and Newton's First Law of Motion?

Inertia is the tendency of an object to resist changes in its state of motion. This is described in Newton's First Law of Motion, which states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force.

4. How do Newton's Second and Third Laws of Motion relate to inertial reference frames?

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law applies in both inertial and non-inertial reference frames. Newton's Third Law of Motion, which states that for every action there is an equal and opposite reaction, also applies in inertial reference frames.

5. Can an object be in multiple inertial reference frames at the same time?

No, an object can only be in one inertial reference frame at a time. However, the choice of reference frame is relative and can change depending on the observer's perspective. This is known as Galilean relativity.

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