Seminar on

MomentsPresented by,

Swati. M. Pujar

BSc VI sem

Roll No: 122

Guided by:

Dr (Smt) S. N. Banasode

MomentsO

A F B

Definition:

Moment of force applied on a rigid body about a point O is defined as the product of force and perpendicular distance of the point from the line of action.

Moment = Force x perpendicular distance

Geometric Representation of Moments

O

A F M B

Moment of force F about O

= OM x F

= OM x AB

= 2 x 1/2 AB x OM

= 2 x area of AOB

Positive and Negative Moments Positive moment

Moment of force turns in anticlockwise direction

F

Negative moment

Moment of force turns in clockwise direction

F

Varigon’s Theorem on Moments Statement

The algebraic sum of moments of two coplanar forces

about any point in their plane is equal to moment of

their resultant about the same point

Proof:

Let R be the resultant of forces P and Q

Two cases arise:

1) P and Q are parallel to each other

2) P and Q are not parallel to each other

Case- 1

P and Q are parallel to each other meeting the line from O at A and B. R is their resultant which meets the line at C

R

Q

P

O A B C

wkt

P x AC = Q x BC

And R = P + Q

Moment of R about O

= R x OC

= (P+Q) x OC

Sum of the moments of P and Q about point O

= P x OA + Q x OB

= P x (OC-AC) + Q x (OC + CB)

= P x OC – P x AC + Q x OC + Q x CB

= (P + Q) OC +0

= (P +Q) OC

= R x OC

= moment of resultant R about a point O

Case – 2

Suppose P and Q meet at a point A

R be the resultant passing through A

O be the point of action

Here AB represents the force P and AD represents the force Q

O D C

R

Q

A P B

Since AOB and ACB stand on the same base and same parallels

ar AOB = ar ACB

Consider ar AOB + ar AOD = ar ACB + ar AOD

= ar ADC + ar AOD

= ar AOC

2(ar AOB + ar AOD) = 2 ar AOC

Moment of force P about O + moment of force Q about O = moment of force R about O