Page 157 - WCS - Electrical

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P / (AB) = Q / (BC) = A / (AC))

CONVERSE OF TRIANGLE OF FORCES
If three forces acting simultaneously on a point keep it in equilibrium, then their magnitude and direction can
be represented by the three sides of a triangle respectively.

Such as
Three forces P, Q, R act on point A in such a manner that point A is in equilibrium, then the resultant force of P and
Q will be the diagonal AC of the parallelogram ABCD. Therefore, ‘R’ can be represented by AC. BC will be equal
and parallel to AD. Therefore, Qcan be represented by BC. Therefore, P, Q, R all three forces can be represented
by three sides of the triangle ABC respectively.

LAW OF POLYGON OF FORCES
If a number of forces are acting on a point in such a way that they are mutually in equilibrium, then they can be
represented by the arms of a closed polygon.
LAMI’S THEOREM

If three forces, acting on a point, are mutually equilibrium, then each force will be proportional to sine of the angle
between the remaining two forces, Such as-
If three forces P, Q, Rare acting on a point are in equilibrium and the angles opposite to them are α, beta , then P/
(sin alpha) = Q/(sin beta) = A/(sin gamma)
MOMENT OF INERTIA
The moment of a force about a point is the product of the force and perpendicular distance between the point and
the line of action of the force
Let F = f Force and x = 1 perpendicular distance Moment of a force = Force x Perpendicular distance M =F.x This
moment is also called as first moment of force. this moment is again multiplied by the perpendicular distance
between the point and the line of action of the force i.e., (Fx)(x) = F * x ^ 2 then this quantity is called as moment
of the moment of a force or second moment of force or moment of inertia.

RADIUS OF GYRATION
The radius of gyration of body is the distance from the axis of reference where the whole mass (or area) of a body
is assumed to be concentrated
CENTRIPETAL FORCE
A body moving in a circle or along a circular path with a onstant velocity, suffers a continuous change in its
direction at every point of its motion. Therefore some force must act at right angles to the direction of motion at
every point, which should change the direction of motion of the body leaving the speed uniform. Thus the force
which acts along the radius of the circle at every point and is always directed towards the centre of the circle,
along which the body moves is known as centripetal force.

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CITS : WCS - Electrical - Exercise 13