This document discusses key concepts in engineering mechanics including units, dimensions, Newton's laws of motion, and vector representations of forces. It covers topics like the parallelogram law, triangle law, vector operations of addition, subtraction, dot and cross products. It also discusses concepts like coplanar forces, rectangular components, particle equilibrium, equivalent force systems, and the principle of transmissibility.

1. presented by
Aadithyan.M , Ajith Moorthi.T , Arun Dev.K.N
Mechanical-1
Government College Of Engineering , Salem-11

2.  Introduction
 Units and Dimensions
 Law of mechanics
 Lami’s theorem
 Parallelogram and triangle law of forces
 Vector representation of forces
 Vector operations of forces
(a) addition
(b) subtraction
(c) dot product
(d) cross product

3.  Coplanar forces
 Rectangular component
 Equilibrium of a particle
 Equilibrium of particles in space
 Equivalent system of forces
 Principle of transmissibility

5. To deal with the above situations ,we need to know about engineering
mechanics
Mechanics is the foundation of most engineering sciences
and is an indispensible to their study.
Mechanics is the science which describes and predicts the
condition of rest or motion of bodies under the action of forces

6. Mechanics: The actions and effects of forces on bodies.
Statics Dynamics
Statics: bodies at rest or in equilibrium
Dynamics: bodies in motion or out of equilibrium
Mechanics

7. Dynamics
(i) Kinematics: Study of motion without reference to forces
producing motion .
(ii) Kinetics: Relation between unbalanced forces and the change
in motion they produce. Weight , friction, Aerodynamic drag these are
the forces involved to produce motion.
E.g. Roller coaster

8. UNIT: a physical quantity that can be counted or measured using
standard size defined by custom or law.
Dimension: It is from a Latin word “measured out” . It a parameter pr
measurement required to define the characteristics of an object.
E.g.: length , width , height.
 If a unit is officially accepted , it’s called Standard unit.
 Group of unit and combination is called System of units. E.g. SI units,
British Units
SI= International Systems of Units
 SI Unit is also called Metric System.

10. Basic Laws of Mechanics
• Newton’s first law: It states that every body continues in its state of rest
or of uniform motion along a straight line unless it is compelled by an
external force to change that state.
• Newton’s second law: it states that the rate of change of momentum of a
body is directly proportional to the external force applied on it direction
of the force.
Fαdp/dt ⇒ F=ma

11. • Newton’s third law: It states that for every action there is an equal and opposite
reaction.
Parallelogram law of forces
It states that “If two forces acting simultaneously on a particle be represented
in magnitude and direction by the two adjacent sides of the parallelogram , then
their resultant may be represented in magnitude and direction by the diagonal
of hr parallelogram which passes through their point of intersection”.
Resultant, R=√ P2+Q2+2PQcosө
Angle, tan Ө= Qsinө/P+Qcosө

12. Triangle Law Of Forces
It states that ,” if two forces acting simultaneously on a particle, be
represented in magnitude and direction by the two adjacent sides of a triangle,
taken in order, their resultant may be represented in magnitude and direction
by the third side of the triangle, taken in opposite order”.
R=P+Q

13. A force vector is a representation of a force that has both magnitude and
direction . A vector is typically represented by an arrow in the direction of the
force and with a length proportional to the force’s magnitude.

14. Addition subtraction Dot Cross
product product
Vector addition of forces:
The net force is the vector sum of all the forces. That is the net
force is the resultant of all the forces; it is the result of adding all the forces
together as vectors. For the situation of the three forces on the force board, the
net force is the sum of force vectors . A+B+C
Vector operation

15. Vector subtraction of forces;
When we think of vector subtraction , we must think about it in
terms adding a negative vector. A negative vector is the same magnitude of the
original vector , but its direction is opposite . In order to subtract two vectors ,
we can use either the triangle method or the parallelogram method from above.

16. Vector dot product of forces :
A dot product is where you multiply one vector by the
component of the second vector , which acts in the direction of the first vector .
In the first equation, the angle is the angle between the two vectors. The
common and important example of dot product is calculating work: force
multiplied by displacement.
Vector cross product of forces;
The vector or cross product is another way to combine two
vectors; it creates a vector perpendicular o both it the originals. In vector form ,
torque is the cross product of the radius vector(from axis of rotation to point of
application of force) and the force vector.

17. When all forces are acting in the same plane , they are called
coplanar
Concurrent Forces:
When forces acting at the same time and at the same point
they are called concurrent forces.

19. The parts of the vector resolved into vertical and
horizontal vectors are rectangular components . Rectangular
components are perpendicular to each other

20. According to Newton’s first law , a particle is said to be in
equilibrium if there is no net force acting on it.
this does not mean that no forces act on the particle, but rather
that the resultant of all the forces which do not on the particle is zero.
Examples of equilibrium:

21. When a particle is in space , the forces acting on the rigid body or on
the particle may be concurrent or non concurrent . If the forces acting
are concurrent, then the equation of equilibrium are ,
∑Fx=0, ∑Fy=0, ∑Fz=0
ie, the resultant force in x , y and z directions are zero.
But if forces acting are non concurrent then the resultant force
in x , y and z direction should be zero also the resultant moment about
x ,y, z axis should be zero
∑Fx=0, ∑Fy=0, ∑Fz=0
∑Mxy=0, ∑Mxz=0, ∑Myz=0

22. Two forces system are said to be equivalent, when they have same resultant in
magnitude, direction and line of action.
ie , the two force systems must have some x and y components of resultant
and same moment about any point in the plane.
(Rx)1=(Rx)2 ; (Ry)1=(Ry)2 and M1=M2
A non concurrent force system or a single force can be replaced by
(i) Two parallel forces , (ii) Two or three non parallel force

23. Acoording to principle of transmissibility of forces, the force can be
transmit from one pint to another point on its line of action without causing any
change in the motion of the object.