Clas Blomberg - Physics of life-Elsevier Science (2007)

20 Part II. The physics basis
Let us see how the picture of the world according to Newtonian mechanics is built up. The
basic concept is motion. A main idea is that any object that moves with a constant velocity
continues that motion unless it is influenced by a force. This is expressed in a more general
concept, the momentum of motion, which is equal to velocity multiplied with mass. In this
description, a mass provides a resistance to motion—the heavier an object is, the more difficult
it is to move it and to achieve large velocities. The mass is also what is relevant for
gravitation forces. It is easy at this point to run into circular definitions, so let us simply
define mass as the basic contents of matter—primarily the sum of the masses of the atomic
nuclei. That works well for our purposes.
The momentum of motion can be generalised to a group of several molecules and then
be a (vector) sum of the various velocities multiplied by the respective masses. Without the
influence of a force, the momentum of motion is kept constant. This is also valid for a group
of objects that may interact with each other but which are not influence by further, external
forces. In that respect, it is relevant for describing an encounter of two particles. In accordance
of this, we can say that a force can be apprehended as something that changes a constant
motion (momentum of motion).
This is how it is presented in basic courses of mechanics. One normally also starts with
an ideal picture of motion in an empty room (that is the only possibility to avoid friction
forces). There are obvious examples when that is relevant. Planets move in essentially empty
space, influenced by a large force from the sun that forces the planets in elliptical, nearly
circular orbits, but also influences form other planets. To the other extreme in size, the molecules
in air move most of the time in straight lines with constant velocities in what is apprehended
as empty space. That motion is changed by rare encounters (collisions) between
particles. The principle of momentum of motion is relevant for the relation between velocities
before and after the encounter.
Before going further to see more of forces, let us say more about various kinds of
motion. An object can move in three different directions, up/down and in two horizontal
directions. It can also rotate. Earth goes around the Sun in a large elliptic orbit, but it also
rotates around its axis, one turn per 24 h. There are three perpendicular axes for every
object and there can be rotations around any or all of the axes. Thus, an object can move in
three directions and rotate around three axes. These motions are independent of each other.
The daily rotation of the Earth is independent of the yearly orbit around the Sun. When this
is said, it can be easy to accept the statement, but this is intricate and not what one intuitively
expects.
This can be demonstrated by an example, often used here to illuminate the situation.
Consider two persons equipped each with a bullet. One of them just drops his bullet, while
the other one shoots his bullet by a rifle held strictly horizontal. The landscape shall be considered
as completely flat. The question is: which bullet reaches the ground first? Is this a
trivial example? Well, hardly anyone who gets this question and hasn’t heard about Newtonian
principles of motion, the principles we just speak about, gives the correct answer. The bullet
goes away horizontally with a high velocity, but it drops also towards the ground, and that
part of it motion is completely independent of the horizontal motion. The bullets reach the
ground at the same time.
A rotational motion has a concept corresponding to the momentum of motion, the angular
momentum, which is the sum (possibly integral) of the product of mass, velocity and distance