The
History of
Dynamics
The Greeks
Natural motion was caused
by some internal quality of
an object that made it seek a
certain “preferred” position
without any application of
force.
The Greeks
Unnatural motion was
anything else.
Unnatural motion was
thought to require applied
force to be sustained.
The Greeks
Natural motions were divided
into two categories:
Terrestrial (near the earth)
Celestial (in the heavens)
The Greeks
Aristotle taught that an
object’s “heaviness”
determined how “vigorously”
it sought its natural place.
Galileo
• began by collecting facts
and establishing a
description of motion
• This is called kinematics.
• Galileo then inductively
developed workable
theories of dynamics.
Galileo
• Experiments showed that
the rate at which an object
falls is not proportional to
its size or mass.
• Astronauts later verified his
theory on the moon.
Ad hoc
a hypothesis based on
conjecture rather than
observation, usually in an
attempt to explain a natural
phenomenon
Inertia
• Galileo’s experiments of
“unnatural” motion
indicated that the “natural”
state of motion of an object
could include moving as
well as resting.
Inertia
Galileo’s Principle of Inertia:
An object will continue in its
original state of motion
unless some outside agent
acts on it.
Inertia
A moving object does not
require a continuous push to
maintain a constant velocity!
A push causes a change in
an object’s motion.
Newton
•
•
•
•
built on the work of others
studied gravitation
Principia
only in recent decades have
scientists discovered any
exceptions to his work
Forces
Summing Forces
• Forces are often
described as “pushes”
and “pulls.”
• Forces are vectors.
• Forces can be added just
as vectors are added.
Summing Forces
• Notation:
ΣF ≡ F1 + F2 + ... + Fn
• The Greek capital letter
sigma (Σ) is used to
indicate a sum.
Summing Forces
• If forces are balanced...
ΣF = 0
• ...and no change in
motion will occur.
ΣF = 0 ↔ ΣFx = 0 and ΣFy = 0
Unbalanced Forces
• will change an object’s
state of motion
• there may be two, or
more than two, forces
which are unbalanced
Unbalanced Forces
• To find the sum of
unbalanced forces, you
add the force vectors
acting upon the object.
• This usually involves
finding and adding the
vector components.
Equilibrant Force
• a force that balances one
or more other concurrent
forces
Equilibrant Force
• a vector having the same
magnitude as the vector
sum of the other
unbalanced forces but
pointing in the opposite
direction
Fequil. = -ΣFother
Equilibrant Force
• If the sum of all forces on
an object is zero, then
any unknown force must
be the equilibrant of all
the known forces.
Weight
• the force of gravity acting
on an object
• a vector pointing straight
downward
• often notated Fw
Types of Forces
• All forces are classified
as either fundamental
forces or mechanical
forces.
• There are four
fundamental forces.
Fundamental Forces
• Gravitational force
• proportional to the
masses of interacting
objects
• can exert its influence
over theoretically
infinite distances
Fundamental Forces
• Gravitational force
• all objects exert
gravitational force on
all other objects
Fundamental Forces
• Electromagnetic force
• used to explain both
magnetism and
electricity
• a long-range force
• a short-range force
Fundamental Forces
• Strong nuclear interaction
force
• Weak nuclear interaction
force
Classification of
Forces
• Noncontact Forces
• gravity
• electromagnetic forces
• sometimes called
“action-at-a-distance”
forces
Classification of
Forces
• Noncontact Forces
• field theory attempts to
explain these
• virtual particles have
been offered as an
explanation
Classification of
Forces
• Contact Forces
• transmitted only by
physical contact
between objects
• include the following:
Classification of
Forces
tensile (pull things apart)
compressive (push things
together or crush)
torsion (twist)
Classification of
Forces
friction (oppose motion
between two objects in
contact)
shear (cause layers within
matter to slide past one
another)
Measuring Forces
• instruments used include:
• spring scale
• load cell
• pressure gauge
Measuring Forces
• instruments used include:
• ballistic pendulum
• accelerometer
• force table
Newton’s
Laws of
Motion
Newton’s Laws
These are the central
principles of dynamics.
Their proper use requires an
understanding of what a
system is.
Systems
In physics, a system is
whatever is inside an
imaginary boundary chosen
by the physicist.
It is isolated from its
surroundings.
Newton’s
st
1
Law
A system at rest will remain
at rest, and a moving system
will move continuously with
a constant velocity unless
acted on by outside
unbalanced forces.
Newton’s
st
1
Law
If all external forces on a
system are balanced, then its
velocity remains constant;
the acceleration is zero.
Newton’s
st
1
Law
If all forces acting on a
system are not balanced,
then a nonzero resultant
force exists and the velocity
changes, resulting in an
acceleration.
Newton’s
st
1
Law
Stated mathematically:
ΣF = 0 ↔ a = 0
or equivalently:
ΣF ≠ 0 ↔ a ≠ 0
Newton’s
st
1
Law
Friction is a force that
causes motion to change.
Inertia is the tendency for a
system to resist a change in
motion.
Newton’s
st
1
Law
Mechanical equilibrium
occurs when the sum of all
forces on a system is zero.
Without unbalanced forces,
objects tend to move in
straight lines.
Newton’s
nd
2
Law
• the most general of the
three laws
• gives a working definition
of force and a way to
measure such force
Newton’s
nd
2
Law
The acceleration of a system
if directly proportional to the
sum of the forces (resultant
force) acting on the system
and is in the same direction
as the resultant.
Newton’s
nd
2
Law
Stated mathematically:
ΣF
a= m
or equivalently:
ΣF = ma
Newton’s
nd
2
Law
A resultant force of 1 N,
when applied to a mass of
1 kg, produces an
acceleration of 1 m/s².
This is how the Newton, a
derived unit, is defined.
Newton’s
nd
2
Law
component equations:
ΣFx = max
ΣFy = may
ΣFz = maz
Newton’s
rd
3
Law
If system X exerts a force
on system Y, then Y exerts
a force of the same
magnitude on X but in the
opposite direction.
FX→Y = -FY→X
Newton’s
rd
3
Law
• forces have four properties
that relate to this law:
• All forces occur in pairs.
• Each force in an actionreaction pair has the
same magnitude.
Newton’s
rd
3
Law
• Each force acts in the
opposite direction in line
with the other force of the
pair.
• Each force acts on a
different system.
Weight and Mass
• The force of planetary
gravitational attraction on
an object is called its
weight, Fw.
• Weight is directly
proportional to mass.
• Fw = am
Weight and Mass
• Since this gravitational
acceleration is downward:
• Fw = mg
• g = -9.81 m/s²
• The magnitude of an
object’s weight vector is
|mg|.
Weight and Mass
• The weight vector, like the
gravity vector, points
straight down (toward the
center of the earth).
• In scalar component form:
• Fwy = mgy
Weight and Mass
• Mass is measured on
scales and reported in units
of kg or g.