Mechanics

Original equation of Newton’s second law

Newton’s Second Law was not stated with the commonly used equation, but was defined in terms of momentum and momentum.

This is the mathematical formula that transcribes Newton’s Second Law
When it comes to Newton’s Second Law , textbooks usually state it as follows: the resultant force acting on a body is the product of the body’s mass and its acceleration . Therefore, we have the following equation:

R = ma

In his famous publication, Philosophiae Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy), of 1687, Isaac Newton did not present the statement quoted above, but he did so as follows:

 

“ The variation of motion is proportional to the applied driving force; and occurs in the direction of the line along which the force is applied”

Isaac Newton

Note that in the original definition, mass and acceleration are not mentioned. What Newton calls driving force we understand today as the product of the force applied to a body by the time interval of force application, that is, the impulse. If we understand change in motion as change in momentum, Newton’s Second Law becomes similar to the impulse theorem. Starting from this theorem, we can arrive at the commonly used statement of this important law. Look:

From the impulse theorem , we have: I = ΔQ;

Since Q = mv, we can write: I = mv – mv 0 ;

Replacing the impulse by the product of the force with time interval and putting the mass in evidence on the right side of the equation, we arrive at:

R .Δt = m.(v – v 0 )

R = m.Δv
        Δt

Knowing that acceleration is the result of the ratio between the change in velocity and the change in time, we finally arrive at the famous statement of Newton’s second law:

R = ma

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