chapter 2 review of
elementary dynamics
The purpose of this chapter is to review some of the laws of dynamics and
to reorganize certain material. In some cases the generality required by
classical dynamics is replaced by special cases peculiar to the gyroscope.
The underlying purpose of this approach is to channel the reader's
knowledge in order to readily understand the nature of the generalized
gyroscope and to set the stage for the subsequent treatment of gyrodynamics.
2.1
NEWTON'S
LAWS
first law.
Every particle remains at rest or moves at a
constant velocity in a straight line unless it is compelled by a force to
change. (This is the property of matter often referred to as inertia.)
newton's second law. A force (or the resultant of a system of forces)
newton's
acting upon a particle accelerates the particle in the direction of the force.
The magnitude of this acceleration is proportional to that of the force.
linear momentum. The linear momentum of a particle is given by the
product of its mass and its linear velocity. If the mass of the particle is
constant,
its linear momentum
is proportional to its velocity.
If
the
velocity changes, its momentum changes proportionally.
Since change of velocity constitutes acceleration, we can restate Newton's
Laws in terms of momentum.
newton's first law. The linear momentum of a particle remains
constant unless compelled by a force to change (conservation of linear
momentum).
newton's second law.
A force (or the resultant of a system of forces)
acting upon a particle changes its momentum vector. The direction
of the