You can explore this history-oriented lesson by Prof. Michael Fowler.
In 530 A.D., working in Alexandria, Byzantine philosopher John Philoponus developed a concept of momentum in his commentary to Aristotle’s Physics. Aristotle had claimed that everything that is moving must be kept moving by something. For example, a thrown ball must be kept moving by motions of the air.
Most writers continued to accept Aristotle’s theory until the time of Galileo, but a few were skeptical.
Philoponus pointed out the absurdity in Aristotle’s claim that motion of an object is promoted by the same air that is resisting its passage.
He proposed instead that an impetus was imparted to the object in the act of throwing it.
Ibn Sina (Arabic ابن سینا) (known by his Latinized name, Avicenna) read Philoponus and published his own theory of motion in The Book of Healing in 1020. He agreed that an impetus is imparted to a projectile by the thrower – but unlike Philoponus, who believed that it was temporary, and would decline even in a vacuum – Ibn Sina viewed it as a persistent. He understood that it required external forces – such as air resistance – to dissipate it.
These ideas were refined by European philosophers Peter Olivi and Jean Buridan. Buridan, who in about 1350 was made rector of the University of Paris, referred to impetus as proportional to the weight times the speed.
Like Ibn Sīnā, Buridan held that impetus (momentum) would not go away by itself; it could only dissipate if it encountered air resistance, friction, etc.
René Descartes believed that the total “quantity of motion” in the universe is conserved: quantity of motion = size and speed.
But Descartes didn’t distinguish between mass and volume, so this is not a specific equation.
Leibniz, in his “Discourse on Metaphysics”, gave an experimental argument against Descartes’ idea of “quantity of motion”.
Leibniz dropped blocks of different sizes, different distances.
He found that [size x speed] did not yield a conserved quantity.
The first correct statement of conservation of momentum:
English mathematician John Wallis, 1670
Mechanica sive De Motu, Tractatus Geometricus:
Isaac Newton’s Philosophiæ Naturalis Principia Mathematica, 1687
Defined “quantity of motion”, as “arising from the velocity and quantity of matter conjointly”
-> mass x velocity – which identifies it as momentum.
Adapted from “Momentum.” Wikipedia, The Free Encyclopedia. 2 Oct. 2015.
2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-2. Use mathematical representations to show that the total momentum of a system of interacting objects is conserved when there is no net force on the system. Emphasis is on the qualitative meaning of the conservation of momentum and the quantitative understanding of the conservation of linear momentum in
interactions involving elastic and inelastic collisions between two objects in one
HS-PS2-3. Apply scientific principles of motion and momentum to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision. Clarification Statement: Both qualitative evaluations and algebraic manipulations may be used.
Common Core Math
- CCSS.MATH.CONTENT.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
- CCSS.MATH.CONTENT.8.EE.C.7 Solve linear equations in one variable
- CCSS.MATH.CONTENT.HSA.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
- CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.