2. Definition of Equilibrium
Equilibrium is the condition of a system
when neither its state of motion nor its
internal energy state tends to change
with time.
3. Definition of Equilibrium
A simple mechanical body is said to be in
equilibrium if it experiences neither linear
acceleration nor angular acceleration; unless
it is disturbed by an outside force, it will
continue in that condition indefinitely. For a
single particle, equilibrium arises if the
vector sum of all forces acting upon the
particle is zero.
4. Terms associated with Equilibrium
•A Force is a push or a pull.
•Net Force is the combination of all forces acting on
an object.
•Tension is the stretching force (springs, rubber
bands, etc.) The stretched spring is under the
"stretching force” called tension.
•Support force is the upward force that acts opposite
the force of gravity.
•Weight is force of gravity pulling on the mass of an
object.
•Vector is an arrow that represents the magnitude and
direction of a quantity.
5. •Vector Quantity needs both magnitude and direction for
a complete description.
•Scalar Quantity can be described by magnitude only, it
has no direction.
•Torque is a ‘turning force’. (τ) –”tau”.
•A Couple is a pair of forces that have the same size but
opposite direction.
•A Lever is a bar that is free to pivot or turn at a fixed
point.
The fixed point is called the FULCRUM.
Terms associated with
Equilibrium
6. Applications of Equilibrium
•Luggage compartment of tour bus is located at
the bottom of the bus and not at the roof.
• Passengers are not allowed to travel while
standing on the upper part of the double decker
bus.
•Seesaw
•Tug of war
•Paddling the boat
•Support in oil ring
8. Conditions for Equilibrium
Static equilibrium is defined as a state where an
object is not accelerating in any way.
There are two conditions for the equilibrium of a
rigid body;
•If a rigid body is in Static Equilibrium, it is at rest,
no translational acceleration and no rotational
acceleration. Both of the following must be true
for anybody in static equilibrium.
9. Conditions for Equilibrium
Translational Equilibrium
An object is in translational equilibrium if it is not
accelerating.
1. Translation equilibrium applies that the
resultant external forces applied to the object is
zero.
Translational equilibrium means;
∑F=0
10. Conditions for Equilibrium
Rotational Equilibrium
An object is in rotational equilibrium if its
rotational acceleration is zero.
2.Rotational equilibrium implies that the resultant
external torque about any axis must be zero
Rotational equilibrium means;
∑τ=0
11. Types of Equilibrium
Stable Equilibrium
A body is said to be in stable equilibrium if it
tends to return to its original position when
slightly displaced.
12. Types of Equilibrium
Examples are:
a) a cone resting on its base;
b) a racing car with low
centre of gravity and wide
base;
c) a ball or a sphere in the
middle of a bowl.
13. Types of Equilibrium
Unstable Equilibrium
A body is said to be in an unstable
equilibrium if when slightly displaced, it
tends to move further away from its original
position.
14. Types of Equilibrium
Examples are:
a) a cone or an egg resting on
its apex or pointed end;
b) a ball or a sphere resting
on an inverted bowl;
c) a tight-rope walker.
15. Types of Equilibrium
Neutral Equilibrium
A body is said to be in neutral equilibrium if
when slightly displaced, it tends to come to
rest in its new position.
16. Types of Equilibrium
Examples are:
a) a cone or cylinder or an egg
resting on its side;
b) a ball or a sphere on a
smooth horizontal table.
17. Laws of Equilibrium
Newton’s First Law
An object at rest or an object
in motion at constant speed
will remain at rest or at
constant speed in the absence
of a resultant force.
18. Laws of Equilibrium
Transitional Equilibrium
An object is said to be in
Translational Equilibrium if and
only if there is no resultant
force. This means that the sum
of all acting forces is zero.
19. Laws of Equilibrium
Rotational Equilibrium
A body is said to be in
rotational equilibrium when
the sum of torque is zero.
The object in rotational
equilibrium will rotate with
angular velocity which could
be zero.
20. Levers in the human body
•Muscles and bones act together to form levers.
•A lever is a rigid rod ( usually a length of bone)
that turns
• about a pivot ( usually a joint ).
•Levers can be used so that a small force can move
a much bigger force.
•This is called mechanical advantage.
21. Mechanical advantage
Levers can be used so that
a small force can move a
much bigger force. This is
called mechanical
advantage. In our bodies
bones act as lever arms,
joints act as pivots, and
muscles provide the effort
forces to move loads.
23. Bones, ligaments, and muscles are the structures
that form levers in the body to create human
movement.
In simple terms, a joint (where two or more bones
join together) forms the axis (or fulcrum), and the
muscles crossing the joint apply the force to move
a weight or resistance.
Levers are able to give us a strength advantage or
a movement advantage but not both together.
24. Levers can also be used to
magnify movement.
For example, when kicking a
ball, small contractions of leg
muscles produce a much larger
movement at the end of the leg.
25. There are four parts to a lever:-
•Lever: bar which action performs
upon.
•Fulcrum: fixed point lever based
on.
•Load: weight of part, object being
lifted.
•Effort: force applied to lift load.
26. Levers are typically
labeled as first class,
second class, or third
class. All three types
are found in the body,
but most levers in the
human body are third
class.
27. Classes of lever system
First Class
•Fulcrum between load effort .
Second Class
•Load between fulcrum and effort .
Third Class
•Effort applied between fulcrum and load .
32. Factors affecting Torque
•Distance: The distance from
the point of rotation affects
torque in such a manner that
the further you are from the
axis of rotation, the easier it
is to rotate around that
point.
F1
F2
d2
d1
Note: The distance d is also known as
the lever arm.
33. Factors affecting Torque
•Angle: Torque also
depends on the angle at
which the force makes
with the lever arm.
Torque is maximum when
the force makes a 90°
angle with the lever arm.
d
F
θ
θ
34. Factors affecting Torque
•Force: Torque is directly proportional to the
force applied to the lever arm. As the force
increases, so does the torque.
F1
d
F2
d
F2
> F1
τ2
> τ1
35. •Torque is represented using the Greek letter tau as
follows:
τ = Fdsinθ
-Where
F = Force (Newtons)
d = lever arm length
θ = angle that force makes with the axis
of the lever arm
Note: Torque is a vector quantity.
37. Torque
•Torque: is a force that tends
to case rotation.
•Force: is a push or pull upon
an object.
*vector quantity.
38. •The formula of Torque
•The factors effecting the Torque:
1 – The applied force
2 - The value of "r" of which is the perpendicular
distance between the pivot and the line of action of
force.
3 – The angle.
T = F * r * sin(theta)
39. Exercises
Example 1
A mechanic holds a wrench 0.3m from the
center of a nut. How large is the Torque
applied to the nut if he pulls with a force of
200N?
