Download Newton`s Laws of Motion

Summary/Review Notes related to the Ideas called
Isaac Newton’s “Laws of Motion”
Understanding Newton’s “Laws of Motion” is not an easy matter. This
understanding often begins when a student wrestles with Newton’s idea called
Momentum.
An object’s Momentum is its “total quantity of motion”. Momentum is the
product of an object’s mass and its velocity.
Expressed mathematically this is:
ρ=m∙v
Whenever the word “motion” appears in a translation of Newton’s writings, it is
important to remember this definition of Momentum.
Common summary of the ideas:
First Law of Motion:
Objects in motion remain in motion unless acted upon by an outside force;
also, objects at rest remain at rest unless acted upon by an outside force.
Second Law of Motion:
Acceleration is proportional to the causative force & inversely proportional to
the mass upon which the force acts.
(a = F ÷ m, which is often written as F = m • a )
The greater the net force impressed, the faster an object changes.
Third Law of Motion:
To every action there is an equal and opposite reaction.
Nothing can touch without being touched.
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Some more detailed thoughts about the Ideas:
Newton's First Law of Motion
Every body will persist in its state of rest or its state of uniform motion in
a straight line unless that state is changed by forces impressed upon it.
This is often called the Law of Inertia.
(Inertia is a property of all matter…..matter resists having its state of motion changed.
Mass is the measurement of an object’s resistance to change of motion.)
Stated in another way: The momentum of an object will be constant until
an outside force increases or decreases that momentum.
Newton's Second Law of Motion
When an object accelerates, the size of that acceleration is directly
proportional to the force applied, and inversely proportional to the mass
of the body. Further, the acceleration will take place in the same
direction as the applied force.
Expressed mathematically this is:
a=F÷m
Alternatively, it can be written as
F = ma
(In Words: Force is the mass times the acceleration)
In both cases:
F = force applied to a body (e.g., in Newtons)
m = mass of the body (e.g., in kilograms)
a = acceleration the body experiences in response to the force applied (e.g., in
m
)
sec 2
Stated in another way: The rate at which the momentum of an object changes
is proportional to the net force acting on the object, and the change will be in
the direction of that net force.
Expressed mathematically this is:
F = Δρ ÷ Δt
Force, Mass, & Acceleration
The second law has two parts:
A) Quantifies the idea of a force in terms of its effects on a massive body.
•
•
Forces produce accelerations.
The more mass a body has, the less it will be accelerated by a given force.
B) Forces and accelerations have a direction (they are both vectors):
•
Accelerations happen in the same direction as the applied forces.
Newton's Third Law of Motion
The mutual actions of two objects upon one another are always equal in
amount and directed towards contrary parts of the world.
Forces exist in pairs….. “simultaneous” and “mutual” in
effect, “equal” in magnitude, “opposite” in direction.
The third law brings together the first and second laws, which deal with single bodies.
The third law makes clear that “forces” are actually interactions between bodies. Force is
not what one body does…….force is really the way in which two bodies interact with one
another.
•
•
If an apple is placed on a table in our room, the apple pushes down on the table with a
force equal to its mass times the acceleration due to gravity.
If the apple sits stationary (unmoving) while pushing down on the table, the table
must be exerting a force on the apple equal in magnitude and opposite in direction.
For students who would like a look at the original form of the ideas, here they are as Newton
expressed them in Latin which was the scholarly language of his time.
AXIOMATA, SIVE LEGES MOTUS
Lex I
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in
directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare.
Lex II
Mutationem motus proportionalem esse vi motrici impressae, & fieri
secumdum lineam rectam qua vis illa imprimatur.
Lex III
Actioni contrariam simper & aequalem esse reactionem: sive corporum
duorum actions in se mutuo simper esse aequales & partes contrarias dirigi.
from Philosophiae Naturalis Principia Mathematica (authored by Isaac Newton; publ. 1687)
(The Mathematical Principals of Natural Philosophy)