PHYSICS: A BRIEF SUMMARY
MIGUEL A. LERMA
1. Introduction
This is a brief introduction to Physics intended for “the impatient”.
Its purpose is to give a brief summary of a number of core theories in
Physics. Usually it takes several years for a Physics student to learn
these theories, but for some practical purposes all you need to know
can be told in the time it takes to read a booklet like this one.
This work is conceived as a dynamic document, that will be posted
on the web and modified periodically to expand some sections, correct
possible mistakes, and include further subjects of interest. Look for it
at
http://www.math.northwestern.edu/
~mlerma/courses/e11-99s/physics.pdf
Please, send me your suggestions—email address at the end.
2. Mechanics
2.1. Newton’s Laws. Ordinary Mechanics is ruled by Newton’s laws.
The motion of a particle is described by
(2.1) F = ma,
where F is the applied force, m is the mass of the particle, and a =
dv/dt = d2 r/dt2 is the particle’s acceleration, with v being its velocity
and r is position vector.
In coordinates equation (2.1) looks like this:
d2 xi
(2.2) Fi = m (i = 1, 2, 3).
dt2
2.2. Euler-Lagrange equations. Newton’s law as described above is
easy to use in Cartesian coordinates for mechanical problems without
constrains, but it can be generalized in a way that makes it easier to
apply to more general situations.
In one dimension Newton’s law is
(2.3) mẍ − F (x, t) = 0,
Date: July 10, 2013.
1
MIGUEL A. LERMA
1. Introduction
This is a brief introduction to Physics intended for “the impatient”.
Its purpose is to give a brief summary of a number of core theories in
Physics. Usually it takes several years for a Physics student to learn
these theories, but for some practical purposes all you need to know
can be told in the time it takes to read a booklet like this one.
This work is conceived as a dynamic document, that will be posted
on the web and modified periodically to expand some sections, correct
possible mistakes, and include further subjects of interest. Look for it
at
http://www.math.northwestern.edu/
~mlerma/courses/e11-99s/physics.pdf
Please, send me your suggestions—email address at the end.
2. Mechanics
2.1. Newton’s Laws. Ordinary Mechanics is ruled by Newton’s laws.
The motion of a particle is described by
(2.1) F = ma,
where F is the applied force, m is the mass of the particle, and a =
dv/dt = d2 r/dt2 is the particle’s acceleration, with v being its velocity
and r is position vector.
In coordinates equation (2.1) looks like this:
d2 xi
(2.2) Fi = m (i = 1, 2, 3).
dt2
2.2. Euler-Lagrange equations. Newton’s law as described above is
easy to use in Cartesian coordinates for mechanical problems without
constrains, but it can be generalized in a way that makes it easier to
apply to more general situations.
In one dimension Newton’s law is
(2.3) mẍ − F (x, t) = 0,
Date: July 10, 2013.
1
