Newton's Third Law of Motion

to appreciate the principles of mechanics,
the forces and how they guide the motion
of objects, without drawing FBDs.
4. Add up vectorially all the external forces
acting on the system. In some cases this
vector sum may be zero. In that case a
central point of the object, called the
Centre of Mass, to be abbreviated as CM,
will be either stationary or moving with
constant velocity (i.e., constant speed
along a straight line.)
We shall refer to the motion of the CM as
the bulk translatory motion of the system.
If the vector sum of the external forces is
non-zero, then that vector sum F total will be
called the Resultant Force on the system.
The bulk translatory motion of the system
is determined by Newton’s second law of
motion, which can now be written as
M r = F total (2)
where M is the total mass of all the component
parts of the system, and r is the radius vector of
the CM of the system, so that r is the
acceleration of the CM.
We have illustrated Rules 1,2,3 in Figures
1. In the Top Box we have shown three objects
A, B and C interacting with one another, and
forming a system. We assume that this system
of three objects is not subjected to any
“external force”. Individually the objects A, B
and C are moving and accelerating only due to
the forces of interaction among themselves.
In frame (a) we have depicted each one of
them as a single system, by drawing
boundaries (with dotted lines) around each.
The forces of interaction are (F 1 ,F′ 1 ), (F 2 ,F′ 2 ),
(F 3 ,F′ 3 ). The pair of forces within parentheses
are the “equal and opposite” action-reaction
pairs. For example if F′ 1 is the action force,
then its counterpart F 1 is the corresponding
(equal and opposite) reaction force. Similarly if
F 3 is the action force, then its counterpart F′ 3 is
the corresponding (equal and opposite) reaction
force. Note also that we have drawn “shooting”
lines on each one of the three objects indicating
that the objects are all moving objects having
velocities v a , v b , v c respectively.
Each one of the three systems A,B,C is
subjected to the following external forces:
(1) external forces F 1 ,F 2 on A;
(2) external forces F′ 1 ,F′ 3 on B;
(3) external forces F′ 2 ,F 3 on C.
In frame (b) we have clubbed A and B
forming a single system AB. Now it is an
interaction between two systems namely, AB
and C. The only external force on AB is F′, and
the only external force on C is F = −F′.
In frame (c) we have taken A, B and C
together as a single system ABC. There are no
external forces on this system ABC.
We shall now illustrate Rule 4 in the form
of the following equations of motion.
System Net external force on the system Eqn of Motion
A F total = F 1 + F 2 m a ra
= F1 + F 2
B F total = F′ 1 + F′ 3 m b
rb
= F′ 1 + F′ 3
C F total = F′ 2 + F 3 m c rc
= F′ 2 + F 3
AB F total = −F = −(F′ 2 +F 3 ) = F 2 + F′ 3 (m a +m b ) r ab
= F′=−F
ABC F total = 0 (m a +m b +m c ) r abc
=0
(3)
222 Physics Education • July − September 2009