Law of the Conservation of Mass, Energy & Momentum

Law of the Conservation of Mass The mass of a body remains
unchanged by any ordinary physical or chemical change to which it may
be subjected.
Law of the Conservation of Energy The principle of conservation
of energy requires that the total mechanical energy of a system remain
unchanged if it is subjected only to forces which depend on position or
configuration.
Law of the Conservation of Momentum The linear momentum of a
system of bodies is unchanged if there is no resultant external force on
the system. The angular momentum of a system of bodies about a fixed
axis is unchanged if there is no resultant external moment about this
axis.

Fundamental Equation Newton's Law

The basic relation between mass, acceleration,
and force is contained in Newton’s second law of motion. As
applied to a particle of mass, F 5 ma, force 5 mass 3 acceleration.
This equation is a vector equation, since the direction of F must be the
direction of a, as well as having F equal in magnitude to ma. An alternative
form of Newton’s second law states that the resultant force is
equal to the time rate of change of momentum, F 5 d(mv)/dt.

NEWTON’S LAWS

First Law
If a balanced force system acts on a particle at rest , it will remain
at rest . If a balanced force system acts on a particle in motion, it will
remain in motion in a straight line without acceleration.
Secound Law
If an unbalanced force system acts on a particle, it will accelerate
in proportion to the magnitude and in the direction of the resultant.
Third Law
When two particles exert forces on each other, these forces are
equal in magnitude, opposite in direction, and collinear.

SYSTEMS AND UNITS OF MEASUREMENTS

In absolute systems, the units of length, mass, and time are considered
fundamental quantities, and all other units including that of force are
derived.
In gravitational systems, the units of length, force, and time are considered
fundamental qualities, and all other units including that of mass
are derived.
In the SI system of units, the unit of mass is the kilogram (kg) and the
unit of length is the metre (m). A force of one newton (N) is derived as
the force that will give 1 kilogram an acceleration of 1 m/s2.
In the English engineering system of units, the unit of mass is the
pound mass (lbm) and the unit of length is the foot (ft). A force of one
pound (1 lbf ) is the force that gives a pound mass (1 lbm) an acceleration
equal to the standard acceleration of gravity on the earth, 32.1740
ft /s2 (9.80665 m/s2). A slug is the mass that will be accelerated 1 ft /s2
by a force of 1 lbf. Therefore, 1 slug 5 32.1740 lbm. When described in
the gravitational system, mass is a derived unit , being the constant of
proportionality between force and acceleration, as determined by Newton’s
second law.

PHYSICAL MECHANICS DEFINATIONS

Force is the action of one body on another which will cause acceleration
of the second body unless acted on by an equal and opposite action
counteracting the effect of the first body. It is a vector quantity.
Time is a measure of the sequence of events. In newtonian mechanics
it is an absolute quantity. In relativistic mechanics it is relative to the
frames of reference in which the sequence of events is observed. The
common unit of time is the second.
Inertia is that property of matter which causes a resistance to any
change in the motion of a body.
Mass is a quantitative measure of inertia.
Acceleration of Gravity Every object which falls in a vacuum at a
given position on the earth’s surface will have the same acceleration g.
Accurate values of the acceleration of gravity as measured relative to
the earth’s surface include the effect of the earth’s rotation and flattening
at the poles. The international gravity formula for the acceleration of
gravity at the earth’s surface is g 5 32.0881(1 1 0.005288 sin2 f 2
0.0000059 sin2 2f) ft/s2, where f is latitude in degrees. For extreme
accuracy, the local acceleration of gravity must also be corrected for the
presence of large water or land masses and for height above sea level.
The absolute acceleration of gravity for a nonrotating earth discounts
the effect of the earth’s rotation and is rarely used, except outside the
earth’s atmosphere. If g0 represents the absolute acceleration at sea
level, the absolute value at an altitude h is g5g0R2/(R1h)2, where R is
the radius of the earth, approximately 3,960 mi (6,373 km).
Weight is the resultant force of attraction on the mass of a body due to
a gravitational field. On the earth, units of weight are based upon an
acceleration of gravity of 32.1740 ft /s2 (9.80665 m/s2).
Linear momentum is the product of mass and the linear velocity of a
particle and is a vector. The moment of the linear-momentum vector
about a fixed axis is the angular momentum of the particle about that
fixed axis. For a rigid body rotating about a fixed axis, angular momentum
is defined as the product of moment of inertia and angular velocity,
each measured about the fixed axis.
An increment of work is defined as the product of an incremental
displacement and the component of the force vector in the direction of
the displacement or the component of the displacement vector in the
direction of the force. The increment of work done by a couple acting on
a body during a rotation of du in the plane of the couple is dU 5 M du.
Energy is defined as the capacity of a body to do work by reason of its
motion or configuration (see Work and Energy).
A vector is a directed line segment that has both magnitude and direction.
In script or text , a vector is distinguished from a scalar V by a
boldface-type V. The magnitude of the scalar is the magnitude of the
vector, V 5 V.
A frame of reference is a specified set of geometric conditions to
which other locations, motion, and time are referred. In newtonian mechanics,
the fixed stars are referred to as the primary (inertial) frame of
reference. Relativistic mechanics denies the existence of a primary reference
frame and holds that all reference frames must be described
relative to each other.