Physical and Mathematical Definitions.
Idle Theory employs a little simple physics. Most of this is concerned
with the physical concepts of Work and Energy.
Work is done when a force is moved through a distance.
When a mass of 0.5
kilograms is raised 2 metres against the gravitational acceleration
of the earth (9.81 m/s^{2}), 0.5 x 9.81 x 2.0, or 9.81 Joules
of energy is used. (Work and Energy are interchangable terms.)
The potential energy of this mass is 9.81 Joules.
If it is released and allowed to fall back,
its velocity, v, after falling 2 metres will will be 4 x 9.81 m/s,
and its kinetic energy will be 1/2.m.v^{2} = 9.81 Joules.
Thus its potential energy will have been converted into kinetic energy
 energy is conserved.
Quantity 
Equivalent 
Dimensions 
S.I. units 
Mass 

M 
Kilogram (kg) 
Length 

L 
Metre (m) 
Time 

T 
Second (s) 
Frequency 
cycles/unit time 
T^{1} 
Hertz (Hz) 
Area 
length x width 
L^{2} 
m^{2} 
Volume 
length x height x width 
L^{3} 
m^{3} 
Density 
Mass/unit volume 
ML^{3} 
kg/m^{3} 
Velocity 
Distance/unit time 
LT^{1} 
m/s 
Acceleration 
Velocity/unit time 
LT^{2} 
m/s^{2} 
Force 
mass x acceleration 
MLT^{2} 
Newton 
Weight 
mass x gravitational acceleration (terrestrial surface acceleration = 9.81 m/s^{2} = g) 
MLT^{2} 
Kilogram (?) 
Pressure or Stress 
force/unit area 
ML^{1}T^{2} 
Pascal (Pa) 
Moment of Inertia 
mass x length^{2} 
ML^{2} 
kg m^{2} 
Work 
force x distance 
ML^{2}T^{2} 
Joule (J) 
Energy 
Work capacity 
ML^{2}T^{2} 
Joule (J) 
Potential Energy 
mass x gravitational acceleration x height raised 
ML^{2}T^{2} 
Joule (J) 
Kinetic Energy 
1/2 mass x velocity^{2} 
ML^{2}T^{2} 
Joule (J) 
Power 
Work/unit time 
ML^{2}T^{3} 
Watt (W) 
Momentum 
Mass x velocity 
MLT^{1} 

The S.I. (or M.K.S.) system has the kilogram as its unit of mass, not weight.
At the surface of the earth, a kilogram weighs 9.81 Newtons.
Theorem of Pythagoras 
A small square is drawn inside a larger square such that its vertices touch the sides of the larger square. The area of the larger square can be expressed in two ways.
1) Area = (a + b)^{2} = a^{2} + 2.a.b + b^{2}
2) Area = c^{2} + 2.a.b
When areas 1) and 2) are equated
3) a^{2} + b^{2} = c^{2}

Equations of Rectilinear Motion 
1) v = u + a.t 
where
u = initial velocity
v = final velocity
a = acceleration
t = time
s = distance

2) s = u.t + ^{1}/_{2}.a.t^{2}
(s is area under graph) 
3) v^{2} = u^{2} + 2.a.s
(combining 1) and 2)) 
Newton's Laws of Motion 
First Law of Motion: Every object continues in its state of rest or uniform
motion in a straight line unless a net external force acts on it
to change that state.

Second Law of Motion: The rate of change of momentum of an object is
directly proportional to the force applied and takes place in
the direction of the force.
This becomes force = mass x acceleration, p= m.a

Third Law of Motion: To every action there is always an equal and opposite
reaction.

The Laws of Thermodynamics 
Zeroth Law: Suppose that of three bodies A, B, and C, bodies
A and B are separately in thermal equilibrium with body C, then
bodies A and B are in thermal equilibrium with each other.
This permits temperature measurement.

First Law: The change in internal energy of a system is
equal to the the heat absorbed by the system plus the external work
done on the system.
This is a statement the conservation of energy. Energy is neither
created nor destroyed.

Second Law: For an isolated system, only those processes
can take place for which the entropy of the sytem increases or
remains constant.
Clausius' statement of the Second Law: It is impossible to
construct a device that operating in a cycle will produce no
effect other than the transfer of heat from a cooler to a hotter
body. The spontaneous flow of heat from a colder body to a hotter
body is impossible.
Lord Kelvin and Max Planck's statement of the Second Law:
It is impossible to construct a device operating in a cycle
for the sole purpose of extracting heat from a reservoir and
changing it into an equal amount of work without rejecting a part
of the heat. i.e. it is impossible to devise a machine that
converts 100% of heat into work.
The universe is cooling down.

Third Law: It is impossible to reach the absolute zero
of temperature in any physical process.

Newton's law of gravity:
F = G . M_{1} . M_{2} / R^{2}
where F is the gravitational force, G is the gravitational constant, M_{1} and M_{2} are two masses, and R is the distance between them.
Centrifugal or centripetal force:
F = M . R . W^{2}
where M is a mass revolving at radius R from an axis with angular velocity W.
References:
Introductory College Physics. Atam P. Arya. Collier Macmillan.