There are various definitions of an inertial reference frame out there, but only one is really accepted by the physics community.(adsbygoogle = window.adsbygoogle || []).push({});

In some places, you will see an inertial reference frame defined as a a reference frame in which Newton's law of inertia is valid.

In some places, you will see an inertial reference frame defined simply as a reference frame which isn't accelerating.

In some places, you will see an inertial reference frame defined as a reference frame in which all three of Newton's laws are valid.

(This is the standard definition)

In some places, you will see an inertial reference frame defined as follows:

An inertial reference frame is defined as a reference frame in which an object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed, and if a repulsive force acts between two bodies of the same mass, they will acquire equal velocities in equal amounts of time.

What I would like to do in this thread, is discuss inertial reference frames. The reason is this: If someone does not know exactly what an inertial reference frame is, then they certainly don't understand the theory of special relativity, precisely because its fundamental postulate is that the speed of light is c in anyinertial reference frame.

To begin with, consider Newton's laws:

Law of inertia: An object at rest will remain at rest, and an object in motion will remain in motion in a straight line at a constant speed, unless acted upon by an outside force.

Newton's second law: An external force will accelerate an object, and the change in the momentum of the object will be directly proportional to the applied force, and in the direction of the applied force.

Newton's third law: Every action is accompanied by an equal and opposite reaction. In other words, if some object in the universe is acted upon by an external force of magnitude F, then some other object in the universe is simultaneously acted upon by a force of the same magnitude F, but in the opposite direction.

Now, Newton's first and second law can be combined into a single mathematical equation which is this:

[tex] F = dP/dt [/tex]

In the above equation, F is a vector quantity, and P = momentum is also a vector quantity. The definition of momentum is as follows:

P = momentum = mass times velocity = mV

where velocity is a vector quantity. The magnitude of an object's velocity, is its speed in a frame.

This is all you need in order to understand the definition of an inertial reference frame.

An interesting consequence of the definition of an inertial reference frame, is that if frame 1 is an inertial reference frame, and frame 2 is moving at a constant speed relative to frame 1, then frame 2 is also an inertial reference frame, but if frame 2 is accelerating with respect to frame 1, then frame 2 is a non inertial reference frame.

The first issue which I wish to address, is how is it shown that Newton's first and second laws are contained in the single mathematical statement given above?

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# On The Definition Of An Inertial Reference Frame

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