# Newton's 2nd law is really the 3rd law?

## Main Question or Discussion Point

Did Newton accidentally reverse the order of his laws of motion? The 1st law implicitly established the notion of time and conservation of energy. The 3rd law formulated the conservation of linear momentum by

$$m_1v_1 + m_2v_2 = constant$$

the time derivative of this expression is

$$m_1a_1 + m_2a_2 = 0$$

acceleration is defined 1st before the inertial force as stated in the 2nd law.

## Answers and Replies

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Integral
Staff Emeritus
Science Advisor
Gold Member
What difference does it make?

This is similar to the chicken and the egg dilemma of choice. The bottom line is that there has to be an acceleration first before there can be a force. We can even make a generalization that all forces have an underlying acceleration for them to exist. And all of these accelerations can be defined as the time rates of change of velocities which are time rate of change of metrics in multi-dimensional spaces.

But if we adhere to strict rule of definition (a concept's existence is based on the moment of its definition), then Newton's 1st law of motion is really the 3rd, and the 2nd can remain where it is, and the 3rd is really the 1st.

The 1st law mentioned force but did not define it. The 2nd law mentioned an acceleration but did not define it. The 3rd, based on the law of conservation of linear momentum, implicitly, defined mass, velocity, acceleration, and the existence of action and reaction, which asserted the existence of opposite forces.

In answer to this statement, i would have to say who cares as is does not really matter that much and if it does, i do not actually think that this would change the world of physics (i dont actually know if i am correct in saying this, but it is a safe assuption)

Andrew Mason
Science Advisor
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Antonio Lao said:
Did Newton accidentally reverse the order of his laws of motion? The 1st law implicitly established the notion of time and conservation of energy. The 3rd law formulated the conservation of linear momentum by

$$m_1v_1 + m_2v_2 = constant$$

the time derivative of this expression is

$$m_1a_1 + m_2a_2 = 0$$

acceleration is defined 1st before the inertial force as stated in the 2nd law.
One has to remember that when Newton developed his laws of motion, he introduced the concept of 'force' into physics. Mass and acceleration were understood concepts. Force was not. So he first had to define force before he went on to say that forces come in equal and opposite pairs. It would have made no sense to make the third law come before the second.

AM

Antonio Lao said:
Did Newton accidentally reverse the order of his laws of motion? The 1st law implicitly established the notion of time and conservation of energy. The 3rd law formulated the conservation of linear momentum by

$$m_1v_1 + m_2v_2 = constant$$

the time derivative of this expression is

$$m_1a_1 + m_2a_2 = 0$$

acceleration is defined 1st before the inertial force as stated in the 2nd law.
I agree with Integral - what difference does it make? But, since we arguing trivialities, I disagree with your characterization of the the 3rd Law. It is only peripherally associated with conservation of momentum. In fact, I have seen arguments that Newton's Third Law is the only really law in his laws of motion, the other two being merely definitions.

ehild
Homework Helper
Do not forget that differential calculus did not exist before Newton's time. The Principia is not only foundation of Mechanics but also foundation of the underlying Mathematics, calculation with infinitesimally small quantities. See at

http://members.tripod.com/~gravitee/toc.htm.

Acceleration is never mentioned in the three Laws.

"Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon."

"The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed."

"To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts."

ehild

Antonio Lao said:
The 3rd law formulated the conservation of linear momentum by

$$m_1v_1 + m_2v_2 = constant$$

The third law uses the second law in establishing this law of conservation of momentum.

Since the second law states that

$$\vec {F}= \frac{\vec {dp}}{dt}$$

So, if no external forces act, the momentum is conserved.