NEWTON'S LAWS OF MOTION
There are three of them.
They explain the motion of an object as
resulting from the forces acting on the object.
What is a force?
An interaction between TWO objects.
For example, pushes and pulls are forces.
We must be careful to think about a force as
acting on one object
from (or due to ) another object.
Adding Forces
 Forces are vectors (They have both magnitude and
direction) and so add as follows:
 In one dimension, note direction using a + or – sign
then add like scalar quantities (regular numbers with
no direction associated with them)
 Examples:
+3 N
+
+3 N
+
+3 N
=
-3 N
0N
=
+6 N
Newton’s First Law
Consider a body on which no net force acts. If
the body is at rest, it will remain at rest. If the
body is moving with constant velocity, it will
continue to do so.
“Consider a body on which no net
force acts…”
 An important word here is NET. It means “total”
or “sum of all” (forces).
 It is not that no force at all can act on the body. It
is just that all the forces must add to zero (cancel
each other out).
Under this condition
(no net force acting on the body):
•If the body is at rest, it will remain at rest.
•If the body is moving with constant
velocity, it will continue to do so.
What if the body is moving with a velocity which is
not constant? Why isn’t this discussed?
Newton’s Second Law
in One Dimension
Commonly shortened to “F=ma”.
Correctly, it is :



 F  ma,
 F
a
m
Only forces which act on that object affect the
acceleration of the object.
Forces exert by the object on another object do not.
Using Newton’s 2nd Law to
Solve Problems
1. Identify all forces acting on the object
-Pushes or Pulls
-Frictional forces -Tension in a string
-Gravitational Force (or weight = mg where g is 9.8 m/s2)
- “Normal forces” (one object touching another).
2. Draw a “Freebody Diagram”
-draw the object, show all forces acting on that object as vectors
pointing in the correct direction. Show the direction of the
acceleration.
3. Chose a coordinate system.
4. Translate the freebody diagram into an algebraic expression based on
Newton’s second law.
Consider an elevator moving downward and speeding
up with an acceleration of 2 m/s2. The mass of the
elevator is 100 kg. Ignore air resistance.
What is the tension in the cable?
1. Identify Forces: Tension in cable, weight of the
elevator
v 2. Draw freebody diagram
T
a
W=Fg earthelevator.
Note: No
negative
sign
3. Chose coordinate system: Let up be the +y
direction and down –y. Then :
4. Translate the FBD into an algebraic expression. TW = m(-a) so
T-(100 kg)(9.8 m/s2) = (100 kg)(-2 m/s2)
Newton’s Third Law
Whenever one object (object A) exerts a force on
another object (object B), the second object exerts a
force back on the first object.
These forces are ALWAYS equal in magnitude (but
they point in opposite directions).
Such forces are called “Newton’s third law force
pairs”.
Not all forces that are equal and opposite are third
law force pairs.
The forces are on different bodies, so do not add to
zero.