We use two kinds of quantities in mechanics - scalars and vectors.
Scalar quantities are those with which only a magnitude is associated. Examples
of scalar quantities are time, volume, density, energy, and mass. Vector,
quantities on the other hand, possess direction as well as magnitude and must
obey the parallelogram law of addition (to be discussed later). Examples of
vector quantities are displacement, velocity, acceleration, force, moment, and
momentum. Speed is a scalar. It is the magnitude of velocity, which is vector.
Thus, velocity is defined by a direction as well as speed.
Vectors representing physical quantities can be classified as
free, sliding or fixed.
A free vector is one whose action is not confined to or associated
with a unique line in space. For example, if a body moves without rotation,
then the movement or displacement of any point in the body may be taken as a
vector. This vector describes equally well the direction and magnitude of
displacement of every point in the body. Thus, we may represent the
displacement of such a body by a free vector.
A sliding vector has a unique line of action in space but not a
unique point of application. For example, when an external force acts on a
rigid body, the force can be applied at any point along its line of action
without changing its effect on the body as whole, and thus it is a sliding
vector.
A fixed vector is one for which a unique point of application is
specified. The action of force on a deformable or non-rigid body must be
specified by a fixed vector at the point of application of the force. In this
instance of the forces and deformations within the body depend on the point of
application of the force, as well as on its magnitude and line of action.
