This document discusses key concepts related to forces and equilibrium. It defines parallel and perpendicular forces, and explains how forces can be added and resolved into components. It also discusses torque or moment of force, center of gravity, couples, and the conditions required for an object to be in equilibrium. Specifically, it explains that there are three states of equilibrium: stable, unstable, and neutral equilibrium.

1. TURNING EFFECTS OF
FORCES
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2. LIKE AND UNLIKE PARALLEL
FORCES
 A force is push or pull. It is a vector quantity because it has
direction.
 Forces having their line of action parallel to each other are
called parallel forces.
 If the forces are acting on a body are parallel and they are in the
same direction, then these forces are said to be like parallel
forces.
 A tube light is suspended with two strings the tensionT1 and T2
in the string is pulling in the upward direction and parallel to one
another. So it is an example of like parallel forces.
 If the force acting on a body are parallel but direction is opposite
then these forces are said to be unlike parallel forces.
 During the tug of war five students pulling the rope towards right
with a force F1 and at the same time other five boys pulling the
same rope towards left with force F2. the force F1 and F2 are
parallel but opposite to each other these forces are called unlike
parallel forces.
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3. ADDITION OF FORCES
 As force is a vector quantity, therefore it
can not be added, subtracted and
multiplied by ordinary methods.
 Forces are added graphically by a rule
known as head to tail rule.
 A resultant force is a single force that
has the same effect as the combined
effect of all the forces to be added.
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4. RESOLUTION OF FORCE
 The resolution of force is its splitting into two components
which are perpendicular to each other.
 These components are called rectangular components of
force.
 The components of force along x-axis is given by Fx =
Fcos θ and is called horizontal component of the force.
 The component of force along y-axis is given by Fy = Fsin
θ and is called vertical component of the force.
 If rectangular components of a force i.e. Fx and Fy are
known, the magnitude and direction of the force can be
determined by the following relations.
 F=√Fx^2 + Fy^2 and θ = tan^-1 (Fy/Fx).
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5. TORQUE OR MOMENT OF
FORCE
 The turning effect of force is known as torque or moment of force. It
measures the rotational effect of a force.
 Torque is given by the product of force and the perpendicular distance
between the axis of rotation and the line of action of the force.
 POINT OF ROTATION:-
 The point about which a body can rotate is called point of rotation.
 AXIS OF ROTATION:-
 It is the line around which a rigid body rotates.
 LINE OF ACTION OF FORCE:-
 It is the line along which a force acts.
 MOMENT ARM:-
 It is perpendicular distance between the axis of rotation and the line of
action of force
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6. CENTRE OF GRAVITY
 The centre of gravity of a body is the
point at which the whole weight of the
body acts vertically downward through
the centre of earth.
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7. COUPLE
 Two forces with the same magnitude but in
opposite direction with different line of
action are said to form a couple.
 Couple is equal to the sum of two equal
torques at point 0 and are acting in the
same direction, i.e. anticlockwise.
 couple= force × perpendicular distance
between the forces
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8. CENTRE OF MASS
 Centre of mass of a body is a point in the body where, the
applied force will move, the body in a straight line without
any rotation.
 EQUILIBRIUM:-
 A body is said to be in equilibrium if the body is at rest or
moving with uniform velocity.
 When a body is at rest the body is said to be in static
equilibrium e.g. a book on the table.
 When a body is moving with uniform velocity then the
body is said to be in dynamic equilibrium.
 A paratrooper coming down with uniform velocity is an
example of dynamic equilibrium.
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9. CONDITIONS FOR
EQUILIBRIUM
 There are two condition to keep a body in equilibrium.
 FIRST CONDITION OF EQUILIBRIUM/TRANSNATIONAL
EQUILIBRIUM:-
 The sum of forces acting along the positive direction of x-axis must be
equal to the sum of forces acting along the negative direction of x-axis
and the sum of forces acting along the positive direction of y-axis must
be equal to the sum of forces acting along the negative direction of y-
axis.
 “The algebraic sum of all the forces acting along x-axis must be zero
and the algebraic sum of all the forces acting along y-axis must be
zero”.
 ΣFx = 0 and ΣFy = 0
 SECOND CONDITION OF EQUILIBRIUM/ROTATIONAL
EQUILIBRIUM:-
 If the sum of all the torques acting in the clockwise direction is equal to
the sum of the torques acting in the anticlockwise direction, the body is
said to be in rotational equilibrium.
 “A body is said to be in rotational equilibrium, if the algebraic sum of all
torque acting on the body is zero”.
 Σt = 0
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10. States of equilibrium
 There are three states of equilibrium.
 (i) stable equilibrium
 (ii) unstable equilibrium
 (iii)neutral equilibrium
 STABLE EQUILIBRIUM:-
 When the centre of gravity of body lies below point of suspension or support,
the body is said to be in stable equilibrium.
 A book lying on a horizontal surface is an example of stable equilibrium.
 UNSTABLE EQUILIBRIUM:-
 When the centre of gravity of a body lies above the point of suspension or
support, the body is said to be in unstable equilibrium.
 A pencil on its tip or a cone in vertically standing position are example of
unstable equilibrium.
 NEUTRAL EQUILIBRIUM:-
 When the centre of the gravity of a body lies at the point of suspension or
support, the body is said to be in neutral equilibrium.
 EXAMPLE: rolling ball
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