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[tex] m_1v_1 + m_2v_2 = constant [/tex]

the time derivative of this expression is

[tex]m_1a_1 + m_2a_2 = 0 [/tex]

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

- Thread starter Antonio Lao
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- #1

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[tex] m_1v_1 + m_2v_2 = constant [/tex]

the time derivative of this expression is

[tex]m_1a_1 + m_2a_2 = 0 [/tex]

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

- #2

Integral

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What difference does it make?

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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.

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Andrew Mason

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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.Antonio Lao said:

[tex] m_1v_1 + m_2v_2 = constant [/tex]

the time derivative of this expression is

[tex]m_1a_1 + m_2a_2 = 0 [/tex]

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

AM

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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.Antonio Lao said:

[tex] m_1v_1 + m_2v_2 = constant [/tex]

the time derivative of this expression is

[tex]m_1a_1 + m_2a_2 = 0 [/tex]

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

- #8

ehild

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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

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

[tex] m_1v_1 + m_2v_2 = constant [/tex]

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

Since the second law states that

[tex] \vec {F}= \frac{\vec {dp}}{dt} [/tex]

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

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