Newton's Third Law
Forces and Motion

Universal connections

Physics Narrative for 14-16 Supporting Physics Teaching

Connecting up all the stuff in the universe

Newton's grand synthesis of the work of Kepler, Galileo and others who thought about the movements in the solar system was an empirical force law. That is, the universal law of gravitation predicted how the force would change as you varied some physical quantities (masses and separations).

forcegravity = G  ×  mass1  ×  mass2r 2

But it was more than that. It asserted that the same interactions happen everywhere. The same kinds of forces interact everywhere in the universe.

This is why it's worth meeting again here. It links two objects, showing how the force on one varies as a result of the masses of both and the separation of the pair. The constant fixes the size of every such force in this universe.

The relationship was also historically significant as it provided a concrete instance of a force law that worked for both astronomical objects and terrestrial objects. Therefore it further undermined the ancient separation of the unchanging heavens from the changing terrestrial sphere.

The significance of Newton's synthesis

Newton made two giant strides as he created his system of understanding that became known as Newtonian mechanics.

The first was to create a systematic way of conceptualising the world in terms of forces and material points. Once that apparatus was in place, and the re-description completed, then he could put his newly invented calculus of fluxions to work. As we've suggested before, there's a sequence:

acceleration = forcemass

The acceleration accumulates velocity:

Δ velocity = acceleration ×  Δ (time interval)

The velocity accumulates position:

Δ position = velocity ×  Δ (time interval)

The accumulations are a modern way of writing statements linking rates of change: Newton's fluxions were his way of managing relationships between quantities that varied with time.

The second was to invent a successful, universally applicable and empirically tested force law.

From now on, quantified predictions would be universal. Newton's synthesis really broke down the centuries-old divide of the here (what happens all around us on the Earth) from the there (what happened in the heavens). The universalism implied made a stunning difference to how we were able to imagine the very space which we inhabit. In the older, Aristotelian, system, space was very inhomogeneous. In the new, Newtonian, system, it was not only homogeneous, but also characterless – space is simply a blank in which things happen. Contrast this with the older idea, where everything had a natural motion that restored the object to its proper place: so space contained a set of hidden gradients, along which different components (earth, air, fire and water) were inclined to move, according to their character. The Newtonian world is a much simpler place.

There are two very significant implications of this new way of describing the world, still as significant today as when newly minted:

  • Earth is not so special a place: the same rules apply everywhere.
  • You're connected physically, and demonstrably, to everything. And you can now figure out by how much.
  • Given a current situation, you can predict with some precision how it will evolve.
Newton's Third Law
is used in analyses relating to Collisions

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