Momentum Conservation
Law of Action Redefined

Newton originally framed the second law
(acceleration) in terms of momentum, not velocity.
• The rate of change in momentum is proportional to the net
force and the change is in the same direction as the force
Initial
momentum
Rocket: has
momentum
Force:
changes
momentum
Final
momentum:
changed by
the force
 p
F
t
Bounce

A falling ball has a
momentum.


After hitting the floor there
has been a change in
momentum.
The change is due to a force
from the floor.
pf
pi
FN
Two Balls

Two balls fall at the same
rate due to gravity, but with
different momenta.


Ball 1 bounces from the
ground.
Ball 2 bounces from ball 1.
pf2
pi2
pf1
pi1
Two Bodies

When two bodies strike each other they exert a force
on each other.

The forces are equal and opposite.
F12
F21
Momentum Change

If two forces are equal in magnitude, then the
changes in momentum are equal in magnitude.
F12
pf1
pi1
F21 
pi2
pf2
F21
p f 1  pi1
t
F12 
p f 2  pi 2
t
Internal Forces

Two objects can be
considered together.

This is called a system.

The internal forces cancel
out from the law of reaction.

The external forces remain.
F12
Fg2
F21
Fg1
Isolated System

A system with no external forces is isolated.
• Only internal forces that cancel out

The net change in momentum for all internal forces
must be zero.

Total momentum in an isolated system is constant.
• Zero change means constant value
Law of Reaction Redefined

The law of reaction can be defined in terms of
momentum.
• In an isolated system the total momentum is conserved.
total momentum of the rocket
and gas stays the same

 Fint  0

rocket
hot gas is
forced out
reaction force acts
on the rocket
rocket
momentum
increases
 p  CONSTANT
Double Bounce

Initially both balls
go down together
with the same
velocity.

The lower ball
gets a force from
the floor and
changes
momentum.
pi2
pi1

The lower ball
hits the upper
ball and
momentum is
conserved
between the
balls.
pf2
pi2
pf1
pm1
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