MOMENT AND COUPLE

MOMENT OF FORCE

Moment of force may be define as the turning tendency of a body with respect to some point or axis.

It is the force multiple by the perpendicular distance from the point or axis.

MOMENT = FORCE X PERPWNDICULAR DISTANCE

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Moment about point `a’ = f x d

TYPES OF MOMENT

Moment are two types (1.) clock wise moment. (2.) anti clock wise moment

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COUPLE

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If two equal parallel and opposite direction force are acting on a body

Then the turning effect of the body is called couple

It is one of the force multiplied of the distance between them called moment of couple.

Moment of couple = F x D

TYPES OF COUPLE

            (1.)  clock wise couple. (2.) anti clock wise couple.

VARIGNON’S THEOREM OR LAW OF MOMENT OR PRINCIPLE OF MOMENT

STATEMENT

If a number of coplanner force are acting simultaneously on a body or particle ‘the algebraic sum of the moments of all the forces about any point is equal to the moment of their resultant force about the same point.

EXPLANATION

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Moment of all the forces about `A’ ΣM_A = ± f₁x₁ ± f₂x₂ ± f₃x₃…………..

Moment of their resultant about `a’ = R x X

According to varignon’s theorem Rx = f₁x₁ ± f₂x₂ ± f₃x₃…………..

PROVE

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Moment of the force about `A’ M_A = F x X

BC = |F| = F

Area of the ∆ABC = ½ x BC x x = ½ x F x X = ½ x M_A

M_A  = 2 x ∆ABC

From □ABCD

∆ABC = ∆ACD = ∆ABD

Angle , ∆BCD = ∆BCE = ∆ABD

∆EBD = ∆ABE + ∆ABD = ∆ABE + ∆BCE

2 X ∆EBD = 2 X ∆ABE + 2 X ∆BCE

Moment of R about E = moment Qabout E + moment of P about E (proved)