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Newton's Laws of Motion

Updated on February 16, 2015

Newtonian or Classical Mechanics

Classical Mechanics or Newtonian Mechanics is a branch of physics: the study of the movements of bodies or particles that are travelling at speeds small compared to c, the speed of light. For bodies approaching relative velocities of c the more complex relativistic mechanics needs to be used. At low speeds Newtonian mechanics gives a very good approximation.

I shall explain here Newton's Laws of Motion and the basics of Newtonian Mechanics.

Newton's Laws of Motion

Newton's Laws of Motion


Unless a resultant force acts on a body, its velocity will not change

If F = 0, then Δv = 0

(Law I is actually just a special case of Law II)


The rate of change of momentum of a body is proportional to the resultant force that acts on the body


F is proportional to  ---(mv)




F = k ---(mv)



If a body A exerts a force F on another body B, then body B exerts a force F on body A of the same size, along the same line, but in the opposite direction.


Some Maths


Momentum p = mv

Momentum is a vector (is has magnitude and direction) and the change in momentum is found by vector subtraction:

Δp = (final momentum) - (initial momentum)

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Newton's Second Law

Newton's Second Law Explained


The rate of change of momentum of a body is proportional to the resultant force that acts on the body


F = k ---(mv)


where k is a non-dimensional constant.

or F = ma

where a = is the vector, acceleration m/s^2

F is measured in Newtons

m = mass in kg

and k = 1

Science Quiz
Science Quiz

Who was Sir Isaac Newton?

Sir Isaac Newton (1642 to 1727) was most famously a physicist, mathematician and astronomer, but was also an alchemist and theologian who, in later life was warden of the Royal Mint (i.e. Bank of England) He was perhaps the greatest scientist who ever lived whose theories define classical mechanics: gravitation and the three laws of motion, which were undisputed for three centuries. Newton observed that a glass prism splits white light into the many colours that form the visible spectrum and developed a theory of colour and also built the first practical reflecting telescope. He also studied the speed of sound and developed a law of cooling and in mathematics worked on differential and integral calculus (with Leibniz). Newton was educated at The King's School, Grantham then at Trinity College, Cambridge University, where he did most of his mathematics and scientific work. In later life Newton became the warden of the Royal Mint in 1696, in London. Newton invested in the South Sea Bubble early, selling and making a lot of money, but watched the value of the investment go up even more. He invested back in again only to lose most of his money when the bubble burst.

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    • MargoPArrowsmith profile image

      MargoPArrowsmith 6 years ago

      I actually understood some of that!

    • Andy-Po profile image

      Andy 6 years ago from London, England

      @ElizabethJeanAl: Thanks very much. I think I need to add a few more diagrams and examples. What seems easy to us does indeed seem to confuse. I too have taught physics, although just as a private tutor - I was never a school teacher (despite most of the rest of my family being physics, maths or biology teachers and lecturers) I have more recently been teaching the physics of silicon chip design (i.e. solid state physics, quantum tunneling, 3D modeling of electromagnetic fields etc.) but in a more commercial role. I think Newton's laws are best explained to children with experiments. When something is fun it is so much easier to learn from it.

    • ElizabethJeanAl profile image

      ElizabethJeanAl 6 years ago

      I teach physics and physical science. Newton's Laws are basic concepts but the kids always seem to have trouble with then. I've never understood that.

      Thanks for sharing.

    • profile image

      fenellashorty 7 years ago

      Very useful introduction to the laws of Newtonian mechanics