Re: Action and reaction

Mikko <mikko.levanto@iki.fi> wrote or quoted:

Newton's third law does not say that action is always the same as
reaction. It only says so about the action and the reaction in the
same interaction. Another way to say the same is that both action
and reaction is the quantity of the interaction.

  Yes, and a wall is no particle but an extended object.

  FWIW, an attempt at a small tutorial:

  Newton's Third Law: Action and Reaction

  Imagine the world is made of tiny "particles." In physics,
  we often think of these as points - they have no size, no
  shape, just a position. When two particles interact, they push
  or pull on each other with forces.

  Newton's Third Law is very simple but very powerful. It says:

  .------------------------------------------------------.
  | For every force that one particle exerts on another, |
  | there is an equal and opposite force exerted back.   |
  '------------------------------------------------------'

  Let's say we have two particles, which we'll call particle
  "i" and particle "j". The force that particle "j" exerts
  on particle "i" is written as:

f_ij

  And the force that particle "i" exerts on particle "j" is:

f_ji

  Newton's Third Law says:

f_ij = -f_ji

  This means that if particle "j" pushes on particle "i" with
  a certain force, then particle "i" pushes back on particle "j" with
  exactly the same amount of force, but in the opposite direction.

  How Forces Affect Motion: Momentum

  Now, let's see what happens to the motion of these particles.
  In physics, we use a quantity called "momentum" (written as "p")
  to describe how much motion a particle has. The momentum
  of a particle changes when a force acts on it.

  The rate at which the momentum of particle "i" changes is given
  by the sum of all the forces from all the other particles:

d
-- p_i  =  sum of all f_ij
dt         (for all j not equal to i)

  Here,

  - "d/dt" means "the rate of change with respect to time"
  - "p_i" is the momentum of particle "i"
  - "f_ij" is the force on "i" due to "j"
  - The sum is over all other particles "j" (not including "i" itself)

  Adding Up All the Particles

  Suppose we have lots of particles. Let's add up the rate of change
  of momentum for every particle:

d
-- (sum of all p_i)  =  sum of all f_ij
dt

  But here's the trick: For every pair of particles, the forces
  they exert on each other are equal and opposite. So, if you
  add up all the forces for every pair, they cancel out:

f_ij + f_ji = 0

  So, when you add up the right side for all pairs, you get zero!

  Conservation of Momentum

  This means:

d
-- (sum of all p_i)  =  0
dt

  Or, in words:

  .------------------------------------------------------------------.
  | The total momentum of all the particles together does not change |
  | over time.                                                       |
  '------------------------------------------------------------------'

  This is called the "conservation of momentum." It's a deep and
  important idea in physics: In an isolated system (where nothing
  from the outside is pushing or pulling), the total momentum
  stays the same, no matter what the particles do to each other.

  Key Points to Remember

  - Particles are points   They have no size or shape, just a
    position.

  - Action = Reaction    Forces between particles always come
    in equal and opposite pairs.

  - Momentum changes because of forces.

  - Total momentum stays the same   if the system is isolated.
    This is the conservation of momentum.