Applied
Mechanics 


Statics : It describes the concepts of calculating
the components of a force and the moment of a force in addition
with the concepts of a free body diagram.

Kinetics : The science which describes the relation
of force to motion is called kinetics.

Displacement : Displacement of a particle is the vector
change of position.

Simple Harmonic Motion : It is a rectilinear motion
where the acceleration is directed towards a fixed point in
the path and is proportional to the distance between that
point and the moving point.
E.g: The motion of the projection on a diameter of a point
moving with constant speed around a circle.

Displacement : x = r cos
(wt + e)
y = r sin ((wt + e)}

Velocity :
v_{x} = r w sin
(wt + e)
= wy
v_{y} = r w cos
(wt + e)
= wx 
Acceleration : a_{x}
= w^{2} cos (wt
+ w) = w^{2}x
a_{y} = r w^{2}
sin (wt + e) = +w^{2}y

Motion of a Projectile : The trajectory of path of a
particle, is a parabola with coordinates x and y at any time
t. The initial velocity of projection is v_{0}, total
of light is T, and downward acceleration is g. Then
x = (v_{0} cosq_{0})
t
y = (v_{0} sinq_{0})
t  gt^{2} / 2
v = (v_{0}^{2}  2 gy)^{1/2}
v_{x} = v_{0} cosq_{0}
v_{y} = v_{0} sinq
 gt
h = v_{0}^{2} / 2g sin 2q
y = v_{0}^{2} / 2g sin 2q,
T = 2v_{0} / g sin w
If projection is horizontal, i.e., a bomb released from air
plane is level flight.
q = 0, x = v_{0}t;
y = 1/2 gt^{2} 
Pendulum : For a simple pendulum, whose mass is concentrated
at point L distance from the axis, the period of oscillation.
t = 2p (L / g)^{1/2}
For a conical pendulum, h is the height of the cone of
revolution.
t = 2p (L / g)^{1/2}
and the angular velocity
For a compound pendulum, k is the radius of gyration about the
axis and s is the distance between the axis and the centre of
gravity, the length of the equivalent simple pendulum.
L = k^{2} / s 
Rigid Body : A rigid body can be defined as a definite
amount of matter the parts of which are fixed in position
relative to one another.

Mass : It is the quantity of matter contained in it.
The units of mass are kilogram, tonne, slug etc.

Momentum : The product of mass and velocity can be
considered as Momentum.

Work : When the force acting on a body produces body
movement the force is said to work. The work done by force
is given by product of the magnitude of the force and distance
acting on it. The work done by a variable force is equal to
the average magnitude of the force multiplied by the distance
through which it acts.

Moments and Couples : Moment of torque M of a force about
a point or centre of moments is the product of the force magnitude
and the arm or perpendicular distance S from the point to the
action line of the force.
M = F.S 
Principles of Moments  Variations Theorem : The moment
of the resultant of forces about a point in their plane or
about a line is the algebraic sum of the moments of those
forces about the point or line.

Couples : Two equal opposite and parallel forces acting
on a body are known as a couple of which the arm is the perpendicular
distance between the lines of action and the moment is the
product of one of the force magnitude and the arm. The couple
tends to produce rotation.

Resultant of a Couple : The resultant of any member
of couple is another couple.

Representation of couple : A couple may be represented
by a vector with length equal to the magnitude of the moment
and direction perpendicular to the plane of the couple, pointed
the way a right hand screw would advance if turned by the
couple.

Centroid and Centre of Gravity : The centroid of a
system of a parallel forces with a given points of application
is the point through which their resultant will always pass
however the forces may be turned while being kept parallel.

Friction : Friction may be defined as the contact resistant
exerted by one body upon a second body when the second body
moves or tends to move past the first body. Friction is a retarding
force always acting opposite to the motion or the tendency to
move. 
Static and Kinetic Friction : When a block of weight
W is subjected to force P to cause motion the corresponding
frictional resistance F which increases linearly as long as
a body does not move and the frictional force occurs. As the
motion starts, does not remain at maximum value and kinetic
friction ensures. The angle of static friction T is the angle
with the horizontal plane at which sliding of one surface upon
another will begin.
tanq = F / N 
Hydrodynamic Friction : In case of a thick film of lubricant
between the surfaces, the hydrodynamic friction can be represented
as,
F = m VA / h
where m = coefficient of
velocity
h = film
thickness of lubricant
V = relative
velocity
A = area
of contact
For a journal bearing with radius r, length L and clearance
C, this equation becomes.
F = 4p^{2} m
m L / c 
Belt of Coil Friction : The friction opposite the slipping
of belt line or brake band on a pulley or sheave. When power
is transmitted, the tension T_{1}, on the driving
side of the belt is greater than the tension T_{2},
on the driven side. If we neglect the centrifugal force, the
tensions at incipient slipping are related by
T_{1} / T_{2} = e^{tax}
where a is the angle in over the entire arc of contact between
belt and pulley. Power transmitted is
P = (T_{1}  T_{2})V
and maximum power is
P_{max} = T^{2}(e^{fx}  1) = T_{1}(1
 1/e^{fx})  V


