# Laws of Motion

If you are trained in elementary physics and in basic calculus, you’d recognize the image above as summarizing Newton’s laws of motion in simple mathematical equations. The wiki explains:

Newton’s laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:

1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.
3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

Isaac Newton was born on Dec 25th 1642 (O.S.). About him, the wiki notes:

Newton was as an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a “natural philosopher”), widely recognised as one of the greatest mathematicians and physicists and among the most influential scientists of all time. He was a key figure in the philosophical revolution known as the Enlightenment. His book Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687, established classical mechanics. Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus.

I think Dec 25th should be celebrated for this reason.

Economist.

## 7 thoughts on “Laws of Motion”

1. I love Christmas. For the past few years, my family has established a non-written ritual.
1. We eat a fully roasted chicken with grilled vegetables for a meal.
2. We used to pair it with homemade mulled wine (the original red wine was store-bought, but we used to do the post-processing at home). We discontinued this practice after we started total alcohol abstinence.
3. We also visit some old church post afternoon. At that time, the devotees are done with their prayers and gone for the day. We enjoy the decor AND the centuries-old marble plaques, remembering some old incident. They make for fascinating reading. At Bangalore, the trinity church has plaques (dating back to the 1800s). You get to know about a boat capsize in the Bay of Bengal (en route from Calcutta to Madras) or a ravaging maneater at Sunderbans striking terror. I recommend the Bangalore folks visit Trinity Church sometime.

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2. Also Atanu, thanks for the “O.S”. Read about Old Style vs New Style dates on the internet and hence learnt something interesting today.

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3. Lin says:

BTW, Newton and Leibniz developed ‘intuitive’ calculus but the ‘epsilon-delta’ or vigorous version of calculus was started by Cauchy in early 1800s. Here’s an example of more vigorous mathematics:
(-1) x (-1) = +1 —-is a formula learned/memorised by all primary school pupils but it seems the majority of non-math major science/engineering grads can’t prove it off-hand

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1. I could not understand your reference to – * – = +. Is it somehow derivable by calculus of Newton?

I recently started reading a pop-culture math book by Tony Crilly called 50-math-ideas. The book acknowledges the non-triviality of – * – = +.
It goes on to explain a half-proof for the same. Half-proof because it starts with an assumption.

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1. Lin says:

+…say could mean you’ve some money
-….could mean you’ve no money and you’re indebt
0…means you’ve no money nor debt
……….
That ‘formula’ is derived from axioms of real numbers system:
(-1) + (+1) = 0 —–(a) …….. one of the axioms
Multiply both sides of (a) by (+1)
(+1)x(-1) + (+1)x(+1) = (+1) x 0 = 0 —–(b)
Multiply both sides of (a) by (-1)
(-1)x(-1) + (-1)x(+1) = (-1) x 0 = 0 —–(c)
Now (b) – (c) on both sides
(+1)x(-1) + (+1)x(+1) -(-1)x(-1) – (-1)x(+1) = 0 – 0 = 0 —–(d)

By commutative law of multiplication (another axiom): (+1)x(-1) = (-1)x(+1)
So (d) becomes (+1)x(+1) -(-1)x(-1) = 0
1= (+1)x(+1) = (-1)x(-1) ……QED

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1. So simple. But do not remember it deriving, ever.
Thanks, Lin.

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