# Objectives:

To verify the principle of moments

## Purpose:

To prove that the body is in equilibrium when sum of all clockwise moments is equal to the sum of all counter clockwise moments

∑CWM = ∑CCWM

## Apparatus:

• Moment Apparatus
• Weights
• Weigh Hangers
• Graph Paper
• Vernier Caliper/ Measuring Scale

## Related Theory:

#### Moment:

The moment of a force is a measure of its tendency to cause a body to rotate about a specific point or axis. This is different from the tendency of a body to move or translate in the direction of force. In order for a moment to develop, the force must act upon the body in such a manner that the body would again be twist. This occurs every time a force is applied so that it does not pass through the centroid of the body. A moment is due to a force not having an equal and opposite force directly along its line of action.

Imagine two people pushing on a door at the door knob from opposite sides. If both of them are pushing with an equal force then there is a state of equilibrium. If one of them would suddenly jump back from the door, the push of the other person will in no longer have an opposition and the door would swing away. The person who was still pushing on the door created a moment. The magnitude of the moment of force acting about a point or axis is directly proportional to the distance of the force from the point or axis. It is defined as the product of force and the moment arm (d). The moment arm or the lever arm is the perpendicular distance between the line of action of the force and the center of moments. The center of moments may be the actual point about which the force causes rotation. It may also be a reference point or axis about which the force may be considered causing rotation. It does not matter as long as the specific point is always taken as the reference point. The latter case is much more common situation in structure design problems. A moment is expressed in pound-foot, kip- feet, Newton- meters or kilo Newton- meter. The most common way to express a moment is :

Moment = Force x Distance

M = F x d

#### Principles of Moments OR Varignon’s Theorem:

This theorem states that:

“The moment of any force is equal to the algebraic sum of the moments of the components of that force.”

It is very important principle that is often used in order to solve system of forces that are acting at/or within a structure.

#### Experiment

The equipment consists of a circular plate mounted on a wooden frame. It is provided with five screws to support a load each. These screws are numbered as A, B, C, D,and E. The loads are hanged through strings which pass over frictionless pulleys. Loads are placed on each screw with the help of a load hanger. After placing of the loads, the alignment of the string is marked on graph paper. The perpendicular distance of each string is measured from centre point of the plate, which represents as moment arm of that particular load. Each load is multiplied by its distance from the center point to calculate moment. Then moments are summed as clockwise and counter clockwise. Their sum should be same. Maximum of 20 N load should be placed on a string.

#### Procedure:

1. Put weights in hangers.
2. Wait for a while, until equilibrium is produced.
3. Now calculate the perpendicular distances of the string to the centre of circular plate.
4. Now calculate the CW and CCW moments.
5. CW and CCW moments should be equal.

## Calculations and Observations:

 Sr No Clock wise Moment Anticlock wise Moment % Difference F(N) d M=Fd F(N) d M=Fd 1 2 3 4 Ʃ Ʃ 5 6 7 8 Ʃ Ʃ

## Precautions:

1. The centre of moments should be correctly established.
2. The distance should be perpendicular to the line of action of force.
3. The sense of rotation should be noted properly.

An error may be generated if the moment arm measurement is faulty i.e it is not perpendicular. The pulleys should be frictionless.

## Results:

 S.No F(N) ∑CW ∑CCW %Error 1 2

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