Lecture 17: On the Shoulders of Giants:
Isaac Newton and the Laws of Motion
Key Ideas:
- 1st Law of Motion:
- Objects in motion remain in motion unless acted upon by an
outside force.
- 2nd Law of Motion:
- Acceleration is proportional to the force & inversely
proportional to the mass (F=ma)
- 3rd Law of Motion:
- To every action there is an equal an opposite reaction.
Isaac Newton (1642-1727)
Isaac Newton was born in Woolsthorpe in rural England on Christmas Day
of 1642 (Julian, England had not yet adopted the Gregorian Calendar).
- Mother was a widow who remarried after he was born.
- Raised by his maternal grandmother.
- Grew up a solitary boy quite unfit as a farmer.
Quiet, irascible, and solitary as an adult (he never married).
He was always fearful that others would steal from him.
He Graduated from Cambridge in 1665 at the age of 23.
The Plague Years
During the bubonic plague epidemic of 1665-1666, Cambridge closed and
Newton went home to Woolsthorpe.
Spent two years in Woolsthorpe, during which
- Invented the integral and differential calculus.
- Developed the binomial theorem.
- Started fundamental work on optics.
- Formulated his laws of motion & gravitation.
All this in his early 20s. He was publish none of it until
many years later.
Lucasian Professor
In 1669, at age 26, he became the Lucasian Professor of
Mathematics at Trinity College, Cambridge.
- Settled into the life of a Cambridge don.
- Continued fundamental work on optics (including inventing
a novel reflecting telescope that is the prototype of all
modern large telescopes).
- Carried out a variety of experiments in optics and alchemy.
- Was always unprepared for classes and hated to teach.
[Note: the current holder of the Lucasian Professorship is Stephen Hawking]
Principia Mathematica
In 1684, Newton was prevailed upon by Edmond Halley to publish
his work on motion and gravitation.
It took Newton about 3 years to reproduce his earlier work.
Halley paid the publication expenses out of his own pocket,
after wheedling, cajoling, and flattering Newton into finishing
it.
The results were published by the Royal Society of London in 1687 as the
Philosophiae Naturalis Principia Mathematica (Mathematical
Principles of Natural Philosophy).
Newton's Synthesis
The Principia is one of the most important books in
history:
- Lays the foundations of modern physics.
- Completely swept away the last vestiges of the Aristotelian view of
the World.
- Replaced older, empirical descriptions with quantifiable,
physical explanations of the natural phenomena.
Unified all motions into three simple laws.
- Every body will stay in a state of rest or uniform
motion in a straight line unless that state is changed by forces
impressed upon it.
Often called the Law of Inertia.
- Inertia is the property of matter that it resists having
its state of motion changed.
Speed versus Velocity
All motion is composed of two parts:
- Speed (how fast is it going)
- Direction (where is it going)
The combination is called the VELOCITY:
- Velocity = how fast, and in what direction.
Change in motion is acceleration:
- Measures how fast the velocity changes.
- Change can be in speed, or direction, or both!
- The size of an 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:
a = F/m
- In Words: Acceleration is proportional to the applied force
and inversely proportional to the mass.
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
- m = mass of the body (e.g., in kilograms)
- a = acceleration the body experiences in response to the force applied
Force, Mass, & Acceleration
The second law has two parts:
1) 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.
2) Forces and accelerations have a direction:
- Accelerations are be in the same direction as
the applied forces.
Application to Planetary Motion
Planets are continually changing the speed and direction of
their motion as they orbit the Sun.
- Move along ellipses with the Sun at one focus.
- Move the fastest when at perihelion (closest to the Sun)
- Move the slowest when at aphelion (furthest from the Sun)
Why does the speed and direction change?
- They are thus accelerating in response to an
applied force.
What force?
- The Force of Gravity.
- For every force applied to a body, there is an
equal and oppositely directed force exerted in response.
This is commonly re-stated as:
- To every action there is an equal & opposite
reaction.
Forces come in pairs
The third law brings together the first and second laws, which deal with
single bodies.
Unifies them in the case of the interaction between two (or more) bodies
via forces.
- If I set an apple on this table, it pushes down on the
table with a force equal to its mass times the
acceleration due to gravity.
- To hold it stationary (unmoving), the table must be
exerting an equal and opposite upward force.
A Complete Description of Motion
Newton's laws of motion provide a complete, quantitative
explanation of the motions of objects.
- They are simple, easily stated in either words or mathematics.
- Universal Physical Laws that apply to all
moving objects, on the Earth or in the heavens.
- They unify phenomena by explaining everyting with the
same set of self-consistent rules.
The Mathematics of Change
The full mathematical statement of the Newton's Laws of Motion required
the invention of a new mathematical language: the Calculus
Independently invented by Newton & Leibnitz, Calculus is the
mathematics of change:
- Language for describing the change in the velocity of a
moving object with time.
- Sets geometry into motion.
The Calculus provides a powerful framework within which we can explore
the motion of objects, from the fall of an apple, to the orbit of the
planets about the Sun.
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Updated: 2007 October 4
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