1Newtonian dynamics of particles

IA Dynamics and Relativity

1.1 Newton’s laws of motion
We will first state Newton’s three laws of motion, and then discuss them individ-
ually.
Law
(Newton’s First Law of Motion)
.
A body remains at rest, or moves uniformly
in a straight line, unless acted on by a force. (This is in fact Galileo’s Law of
Inertia)
Law
(Newton’s Second Law of Motion)
.
The rate of change of momentum of a
body is equal to the force acting on it (in both magnitude and direction).
Law
(Newton’s Third Law of Motion)
.
To every action there is an equal and
opposite reaction: the forces of two bodies on each other are equal and in opposite
directions.
The first law might seem redundant given the second if interpreted literally.
According to the second law, if there is no force, then the momentum doesn’t
change. Hence the body remains at rest or moves uniformly in a straight line.
So why do we have the first law? Historically, it might be there to explicitly
counter Aristotle’s idea that objects naturally slow down to rest. However, some
(modern) physicists give it an alternative interpretation:
Note that the first law isn’t always true. Take yourself as a frame of reference.
When you move around your room, things will seem like they are moving around
(relative to you). When you sit down, they stop moving. However, in reality,
they’ve always been sitting there still. On second thought, this is because you,
the frame of reference, is accelerating, not the objects. The first law only holds
in frames that are themselves not accelerating. We call these inertial frames.
Definition
(Inertial frames)
.
Inertial frames are frames of references in which
the frames themselves are not accelerating. Newton’s Laws only hold in inertial
frames.
Then we can take the first law to assert that inertial frames exists. Even
though the Earth itself is rotating and orbiting the sun, for most purposes, any
fixed place on the Earth counts as an inertial frame.