पुरातन भारतीय विज्ञानं - Newton's Second law

पुरातन भारतीय विज्ञानं 

the opening for last note was from sulbha sutra with bodhayana's theorem on right angled triangles.Now shall we go into the calculation of value of PI by our vedic scholors and then get back to our physics subsequently. 

Aryabhatta says in his work (aryabhateeyum) : 

" CHATHUR ADHIKAM SHATHAMASHADGUNAM DWISHASHTISTHATHA: SAHASRANAAM 

  AYUTHADVAYA VISHKAMBHYASYASANNO VRUTHTHA PARINAAHA: "  

This is the value of pi given in words. it means 3.146 !!! 

Yet another interesting fact about the science of light. Physics says that sunlight (white light) is split into 7 constituent colours.This fact is mentioned in the RIGVEDA (oldest of the Vedas) it says; 

SAPTHA SURYASYA RASAMAYAHA [RIG VEDA 5.45.9] 

SAPTHA - SEVEN ; SURYA -SUN 

It says. Seven horses draw the chariot of SUN. Meaning its constituents are seven in number.

With this interesting introduction, Let us get back to our Vaisheshika Sutras.

KARMA KARMA SAADHYAM NA VIDYATHE [ VAISHESHIKA SUTRA 1.1.11]

KARMA - Energy NA-Not SADHYAM- Possible

An energy cannot change into another energy without the intervention of work.

Now we shall move into discussing Potential and Kinetic energy by way of VAISHEHSIKA SUTRAS. The following two sutras may sound abstract but their meaning when put together makes sense.They explain the concept with the help of an example. 

ATMA SAMYOGA PRAYATNABHYAM HASTHE KARMA 

Atma- individual ; Prayatnam-effort ; karma - energy ; Hastha- Hand 

Link with an individual and his efforts, Produces energy. 

THATHA HASTHA SAMYOGAATH MUSAALE KARMA 

Work done by hand transfers karma into the body lifted by it. 

When we combine the above sutras, we infer that, 

" When hand lifts a body, although work is done by the hand, yet, the body develops potential energy.this illustrates that work done by one object on another can produce energy in the object " 

ABHIGAATAJE MUSALADOU KARMANI VYAKTHIREKAATH AKAARANAM HASTHA SAMYOGA: [VAISHESHIKA SUTRA 5.1.3] 

MUSALA-Pulverizer ; Akaaranam- not the reason ; Hastha- hand 

The pulverizer hits the base, and rebounds. This is a collision‟ or abhighata”. The energy generated in the pulverizor on account of the „collision‟ is not caused due to contact with hand.

THATHA AATMA SAMYOGO HASTA KARMANI [VAISHESHIKA SUTRA 5.1.4]

And because of same reasons, the link with self is not the cause of (generation of) energy in the hand (following the collision).

RISHI describes a perfectly elastic collision or recoil of polverizer with the base. The pulverizer rebounds while the hand is holding it passively. Maharishi kanada is aware that when the pulverizer hits the base, this action has an equal and opposite reaction. This becomes clear from the following sutras which imply that the pulverizer rises to its original height without any effort by holding hand

ABHIGHATHATH MUSALA SAMYOGAATH HASTHE KARMA [VAISHESHIKA SUTRA  5.1.5]

the two causes of generation of energy is the collision of body (pulorizer) with the base and hands contact with the body. 

ATHMA KARMA HASTA SAMYOGAATH CHA [VAISHESHIKA SUTRA 5.1.6]

in this way, energy generated can be due to the hands connection with the object or due to its link with itself. 

Thus put together : 

Something cannot have movement by its own. The force needs to be exerted on it from outside. The hand in this example, gets motion and thereby energy by different agents external to hand; either by the sefl i.e. force applied by the individual or by force applied on it by rebounding pulverizor.

As we are familiar with this background, now see KANADA,who lived in the BCs give us what is called Newton's Second law known today !!! 

This sutra that we are going to see as the first, we have already discussed, but we will just have a glance at it, because the law proposed by kanada has this as a base.

NODANA VISHESHA ABHAVAATH, NA URDHVAM NA THRAYYAG GAMANAM 

The projectile cannot move upwards or obliquely unless there is an impulse created. 

PRAYATNA VISHESHAAT NODANA VISHESHA:   [ VAISHESHIKA SUTRA 5.1.9]

Prayatna - EFFORT ; NODANA VISHESHA: - Change in momentum 

A particular prayatna ( FORCE X TIME ) Produces a Particular NODAN ( Change of momentum). !!!!! 

Prayatna means the effort of an individual.Total effort is force applied multiplied by the time.Kanada proposes that there is a fixed proportion between prayatna and nodana. 

NODANA VISHESHAATH UDAASANA VISHESHA: [VAISHESHIKA SUTRA 5.1.10]

nodana- Impulse (momentum) ; Udaasana- Rise 

A Particular momentum produces a particular rise of the projectile. 

This can be interpreted with the physics as we know today as ; 

if the body is at rest in the beginning, the momentum attained by it is equal to the nodana (or impulse) applied to it. For a body of given mass, a particular momentum produces a particular velocity. A particular initial velocity produces a particular maximum height attained by the projectile. It can be said thus that a particular impulse produces a particular height in a given projectile

So that explains the Second law of newton proposed by KANADA.Remember that we have already seen the third law in our Previous note and Newton's First law in the first note !!