Newton’s First Law of Motion

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L0 is the distance in the relaxed length, while L is the distance of the entire spring. s is the difference between these two variabels.

Newton's First Law of Motion, commonly referred to as the law of inertia, explains the relationship between the the change of velocity of an object and its interaction with others.

The Main Idea

To be exact, the definition of the First Law of Motion is as follows:

Every body persists in its state of rest or of moving with constant speed in a constant direction, except to the extent that it is compelled to change that state by forces acting on it. 

In other (and much simpler) terms, it means that an object at rest stays at rest and an object in in motion stays in motion at a constant velocity unless acted on by an unbalanced net force. It's important to keep in mind that only a difference in net force can affect the velocity of an object. The amount of change in velocity is determined by Newton's Second Law of Motion.

A Mathematical Model

Newton's first law can be stated mathematically as follows:

[math]\displaystyle{ {\vec{F_{net}} = 0 \Leftrightarrow \frac{d\vec{v}}{dt}} = 0 }[/math]

Where...

[math]\displaystyle{ \vec{F_{net}} }[/math] is the net force from the surroundings.

[math]\displaystyle{ d\vec{v} }[/math] is the change in velocity of the system.

[math]\displaystyle{ dt }[/math] is the change in time of the system

If we trace this formula from the left to the right, we can see that if the net force on an object is zero, then the change in velocity of an object is also zero. Conversely, if we were given an object and told that its change in momentum is zero, then we can deduce that the net force acting on the object is also zero. Keep in mind, however, that this formula simple deals with the change in velocity. It does not mean that the object is at rest, only that its velocity remains constant.

A Computational Model

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Examples

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History

Isaac Newton first described his three laws of motion in The Mathematical Principle of Natural Philosophy, for the Principia, which was published in 1687. These laws described the relationship between an object and the forces acting upon it and laid the foundation for classical mechanics. Newton's first law, in particular, expanded upon the concept of inertia which was discovered by Galileo Galilei years before.

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