This document discusses concepts of moment, friction, and their applications in engineering mechanics. It defines moment as the perpendicular distance from a point to a line or surface, and explains that a moment of force is the product of the distance of a force from an axis times the magnitude of the force. It also discusses Varignon's theorem, the principle of moments, parallel forces, torque, and conditions for equilibrium under forces. The document then defines friction and the laws of friction, limiting friction, and sliding friction. It provides examples of how these concepts are applied in areas like transportation and measurement.

1. .
.
Concept of Moment
& Friction
Course :- Diploma Engineering
Sub :- Engineering Mechanics
Unit :- III

2. Concept of Moment
• In physics, moment relates to the perpendicular distance from
a point to a line or a surface, and is derived from the
mathematical concept of moments.
• A moment of force being the product of the distance of a force
from an axis times the magnitude of the force, i.e., F × d, where F
is the magnitude of the force and d is the moment of the force.
• See torque for a more complete description of moments of force or
couple for the related concept free moment of force also known as
a force couple.
• The moment of inertia is the "second moment" of mass of a
physical object. This is the object's resistance or inertia to changes
in its angular motion. It is roughly the sum of the squared
distances (i.e., moments) of the object's mass particles about a
particular axis.

3. Varignon’s theorem
• Statement only
• The theorem states that the moment of a force
about any point is equal to the sum of the
moments of its components about the same
point.

4. Principle of Moments –Application
of moments to simple mechanism
• The Principle of Moments, also known as
Varignon's Theorem, states that the moment of
any force is equal to the algebraic sum of the
moments of the components of that force.
• It is a very important principle that is often used
in conjunction with the Principle of
Transmissibility in order to solve systems of
forces that are acting upon and/or within a
structure.
• This concept will be illustrated by calculating the
moment around the bolt caused by the 100 pound
force at points A, B, C, D, and E in the
illustration.

5. Parallel Forces
• Statics refers to the bodies in equilibrium.
• Equilibrium deals with the absence of a net force. When the net
equals zero, the forces are in equilibrium provided they are
concurrent (they intersect).
• If they are non-concurrent, the body may rotate even if the
vector sum of the forces equals zero. Hence, there must be
another condition to set forces in equilibrium – that under the
influence of forces, the body must have no tendency toward
translational or rotary motion.
• An example of non-concurrent forces where the vector sum
may be equal to zero but it still causes the body to move is
parallel forces. They act in the same or opposite directions.
Their lines of action are parallel. Forces acting in the same or
opposite directions are parallel.

6. • Torque (Moment Of Force)
• Torque or moment of force refers to the turning
effect of the force upon a body about a point
(fulcrum).
• It is the product of the magnitude of the force and
perpendicular distance from the line of action of
the force to the fulcrum.
• This perpendicular distance is called moment arm
or lever arm. The greater the distance from the
axis to the point where we apply the force, the
greater the torque.
• Maximum torque occurs when the direction of the
applied force is perpendicular to a line drawn
between the axis and the point where the force is
applied.

7. • When the line and the force are in the same
direction, so that the force acts directly toward
or away from the axis of rotation, there is no
torque.
• Mathematical Equation:
Torque = Force X Moment arm
M = F X d

8. Conditions For A Body To Be In Equilibrium
Under The Influence Of Forces
1. The sum of the forces pulling the body in one
direction must equal the sum of the forces
pulling the body in the opposite direction:
ΣF = 0
2. The sum of moments tending to rotate the
body clockwise about a point must equal the
sum of moments tending to rotate the body
counter clockwise about the same point:
ΣM = 0

9. Concepts of Couple Properties and
Effect
• In mechanics, a couple is a system of forces with a
resultant moment but no resultant force. A better term is
force couple or pure moment.
• Its effect is to create rotation without translation, or more
generally without any acceleration of the centre of mass.
• In rigid body mechanics, force couples are free vectors,
meaning their effects on a body are independent of the
point of application. The resultant moment of a couple is
called a torque.
• Torque has special properties that moment does not have,
in particular the property of being independent of
reference point, as described below.

10. Simple couple
• Definition- A couple is a pair of forces, equal in
magnitude, oppositely directed, and displaced by
perpendicular distance or moment.
• The simplest kind of couple consists of two equal
and opposite forces whose lines of action do not
coincide. This is called a "simple couple".
• The forces have a turning effect or moment called
a torque about an axis which is normal to the
plane of the forces. The SI unit for the torque of
the couple is Newton meter.

11. Simple couple
• If the two forces are F and −F, then the
magnitude of the torque is given by the
following formula:
• T = F × d
• where
T is the torque
F is the magnitude of one of the forces
d is the perpendicular distance between the forces,
sometimes called the arm of the couple

12. Simple couple
• The magnitude of the torque is always equal to
F d, with the direction of the torque given by
the unit vector ê, which is perpendicular to the
plane containing the two forces.
• When d is taken as a vector between the points
of action of the forces, then the couple is the
cross product of d and F.
T = d × F

13. Applications
• Couples are very important in mechanical
engineering and the physical sciences.
• In a liquid crystal it is the rotation of an optic axis
called the director that produces the functionality of
these compounds. As Jerald Erickson explained
• At first glance, it may seem that it is optics or
electronics which is involved, rather than
mechanics. Actually, the changes in optical
behavior, etc. are associated with changes in
orientation. In turn, these are produced by couples.
Very roughly, it is similar to bending a wire, by
applying couples.

14. Moving a force parallel to its line of
action
• In physics, net force is the overall force acting on an
object. In order to perform this calculation the body is
isolated and interactions with the environment or constraints
are introduced as forces and torques forming a free-body
diagram.
• The net force does not have the same effect on the
movement of the object as the original system forces, unless
the point of application of the net force and an associated
torque are determined so that they form the resultant force
and torque.
• It is always possible to determine the torque associated with
a point of application of a net force so that it maintains the
movement of the object under the original system of forces.

15. Moving a force parallel to its line of
action
• With its associated torque, the net force becomes
the resultant force and has the same effect on the
rotational motion of the object as all actual forces
taken together.
• It is possible for a system of forces to define a
torque-free resultant force.
• In this case, the net force when applied at the
proper line of action has the same effect on the
body as all of the forces at their points of
application.
• It is not always possible to find a torque-free
resultant force.

16. General Cases of Coplanar Force
System
• Nonconcurrent Force Systems
• You already have some understanding of the
conditions which determine whether a body
subject to nonconcurrent forces is in
equilibrium. Look at the following cases and
tell in which ones
1. Sum of Forces = 0
2. The system is likely to be in equilibrium

17. Friction
• Concept of friction
• Friction is the force resisting the relative motion of
solid surfaces, fluid layers, and material elements
sliding against each other. There are several types of
friction:
• Dry friction resists relative lateral motion of two solid
surfaces in contact. Dry friction is subdivided into static
friction ("stiction") between non-moving surfaces, and
kinetic friction between moving surfaces.
• Fluid friction describes the friction between layers
within a viscous fluid that are moving relative to each
other.

18. Concept of Friction
• Lubricated friction is a case of fluid friction
where a fluid separates two solid surfaces.
• Skin friction is a component of drag, the force
resisting the motion of a fluid across the
surface of a body.
• Internal friction is the force resisting motion
between the elements making up a solid
material while it undergoes deformation.

19. Concept of Friction
• Energy of friction
• According to the law of conservation of energy,
no energy is destroyed due to friction, though it
may be lost to the system of concern.
• Energy is transformed from other forms into heat.
A sliding hockey puck comes to rest because
friction converts its kinetic energy into heat.
• Since heat quickly dissipates, many early
philosophers, including Aristotle, wrongly
concluded that moving objects lose energy
without a driving force.

20. Concept of Friction
• Work of friction
• In the reference frame of the interface between two surfaces,
static friction does no work, because there is never displacement
between the surfaces.
• In the same reference frame, kinetic friction is always in the
direction opposite the motion, and does negative work. However,
friction can do positive work in certain frames of reference.
• Thus, the kinetic friction between the box and rug accelerates the
box in the same direction that the box moves, doing positive
work. The work done by friction can translate into deformation,
wear, and heat that can affect the contact surface properties (even
the coefficient of friction between the surfaces). This can be
beneficial as in polishing

21. Applications
• Transportation
• Automobile brakes inherently rely on friction
• Rail adhesion refers to the grip wheels of a train have on the
rails
• Measurement
• A tribometer is an instrument that measures friction on a
surface.
• A profilograph is a device used to measure pavement surface
roughness.
• Household usage
• • Friction is used to heat and ignite matchsticks (friction
between the head of a matchstick
• and the rubbing surface of the match box).

22. Laws Of Friction
• The Three Laws of Friction
• The frictional force being independent of the
area of contact
• The frictional force being proportional to the
load
• The frictional force being independent of the
speed of movement

23. • The amount of Friction that can be exerted between
two surfaces is limited and if the forces acting on the
body are made sufficiently great, motion will occur.
Hence, we define limiting friction as the friction
which is exerted when equilibrium is on the point of
being broken by one body sliding on another. The
magnitude of limiting friction is given by the
following three laws.
• Law 1
• When two bodies are in contact the direction of the
forces of Friction on one of them at it's point of
contact, is opposite to the direction in which the point
of contact tends to move relative to the other.

24. • Law 2
• If the bodies are in equilibrium, the force of
Friction is just sufficient to prevent motion and
may therefore be determined by applying the
conditions of equilibrium of all the forces
acting on the body.
• Law 3
• The ratio of the limiting friction to the Normal
reaction between two surfaces depends on the
substances of which the surfaces are
composed, and not on the magnitude of the
Normal reaction.

25. Limiting Friction and Coefficient of
Friction
• The maximum value of static friction, when motion is
impending, is sometimes referred to as limiting friction,
although this term is not used universally. we find that the
maximum value of static friction and the force of kinetic
friction are each proportional to the normal force; that is,
fsmax = μs n
and
fk = μk n
• These μ's are called the coefficients of friction. μs is the
coefficient of static friction and μk is the coefficient of
kinetic friction. Since fs,max > fk, this means μs > μk. If it
is clear from context, it is common to say simply the
"coefficient of friction" and to label it merely as μ.

26. Sliding Friction
• Sliding friction is the kind of friction that is caused by two surfaces
that slide against each other. This kind of friction is alternatively
known as kinetic. Sliding friction is intended to stop an object from
moving.
• Understanding Sliding Friction
• The amount of sliding friction created by objects is expressed as a
coefficient which takes into consideration the various factors that
can affect the level of friction. These various factors that can impact
sliding friction include the following:
• The surface deformation of objects
• The roughness/smoothness of the surface of the objects
• The original speed of either object
• The size of object
• The amount of pressure on either object
• The adhesion of the surface

27. CONTENT REFERENCES
 A TEXT BOOK OF ENGINEERING MECHANICS ,
R.S.KHURMI , S.CHAND & COMPANY PVT. LTD.
A TEXT BOOK OF ENGINEERING MECHANICS , Dr.
R.K.BANSAL , LAXMI PUBLICATION

28. Any
Question??

29. Thank
You