8. INERTIA
From the previous chapter it has become clear, that the first Newton's
law, on which one any free body (on which one other bodies do not act) is gone
uniformly and rectilinearly its is fair not to the body,
and to an axis screw trajectory. This axis for a free body is truely
rectilinear. Body, moving on a screw trajectory, is gone uniformly in two
orthogonally related directions: lengthwise axis of screw trajectory and
perpendicularly of this axis. Both these motions are equivalent, therefore have
similar properties.
The circular motion takes place without energy consumption, since in a
radial direction always centrifugal force and attractive force to center of
rotation are balanced and on the second Newton's law a body rest in a radial
direction, and in a tangential direction any forces do not act. In a considered
case inertia (the resistance to change of parameters of motion) will be
exhibited in two cases: 1. At attempt of an alteration
of speed of circular motion, 2. At attempt to change a radius of gyration.
Angular momentum of a body at circular motion:
L=mVr (1), where m - mass of a body, V - its speed, r - radius of
gyration. The formula (1) demonstrates, that inertia - a direct consequent of a
law of conservation of angular momentum of a body concerning center of
rotation. At any attempts to change angular momentum, we are compelled to
expend some energy on boost, braking or change of a radius of gyration.
The translational motion of a free body also takes place without energy
consumption, since any forces do not act on a body. In this case inertia also
is exhibited at: 1. To attempt of an alteration of
speed of translational motion, 2. At attempt to change a current of traffic.
The angular momentum of a body at translational motion of rather any point of
space is determined too by formula (1), where V - speed of translational
motion, r - spacing interval from any point of space up to a line of a current
of traffic. Here too at any attempts to change angular momentum of a body we
under the necessity to spend energy for its boost, braking or reversal of
operation. Said is illustrated on figures 1 (alteration of speed of motion) and
2 (veering of motion), when we affix some efforts for these changes between
points A and B (since because of inertia at once to realise these changes it is
impossible).
For a figure 1: mV1r¹mV2r, where r - spacing
interval from any point (same) space up to a line of a current of traffic. For
a figure 2: mV1r1¹mV1r2,
where r1 and r2 of spacing interval from a line of a
current of traffic up to the same arbitrary point of space. Thus, it is
possible to make a common conclusion: the inertia is demonstration of a
fundamental law of conservation of angular momentum of a body. Rectilinear
motion of a free body and orbital motion of a bound body are inertial motions.
