# How do moments of force affect engineering problems?

In our last article, we looked at how we can apply principles of energy and power to engineering problems. Now we’re going to dive into how moments of force can be applied to engineering problems.

## Moments

If we want to describe a force acting on a body, we need to know the magnitude and direction of that force. The effect of the force on a body is that the particle moves in a straight line without turning.

When a force is applied to a rigid body, then the point of application of the force needs to be given, as well as its magnitude and direction. The force can cause the body to experience a rotational motion, with or without a translation of motion. In other words, the body might now turn as well as moving in a straight line.

Imagine we have two forces of unequal magnitude, but want them to produce the same turning effect about a fixed point. To achieve this, the point of application of the smaller force should be at a greater distance from the fixed point than that of the larger force. You can see a diagram showing this below:

The moment of a force, F, about an axis perpendicular to the plane of the diagram at point O is the product of the force and the perpendicular distance x of its line of action from O.

The diagram shows Moment of F about O = Fx anticlockwise. The units of a moment are Nm, and a moment is sometimes called a torque, T.

## Couple

The moment produced by two equal and opposite parallel forces that don’t act in the same straight line is called a couple. The moment produced by a couple is equal to the product of one of the forces and perpendicular distance between their lines of action.

The moment is independent of the distance, X, and is the same about any point in the same plane. In the image below we can see a wrench. The use of the wrench applies a force, F, at a perpendicular distance from the turning point. In this case the turning point is the centre of the nut. The turning moment, or torque, applied is force x perpendicular distance.

Let’s check out an example to see how this can work. Imagine a pulley wheel with a diameter of 500mm. It has a force of 1000N applied at the rim, and we’re going to work out the torque when this happens.

Torque T = Fr, where force F = 100N and radius r =500/ 2 = 250 mm = 0.25m.

Hence, torque, T = (100)(0.25) = 25 Nm

## Sum of Moments

When several forces are lying in the same plane and act on a body, the moments about any point can be added. We need to take into account the sense of rotation for each moment. Imagine that forces of magnitude three end, 4 N and 5 N are applied to a beam of length 6 metres as shown in the diagram:

Moments about point A, clockwise, can be taken as:

- Moment of the 3N force about A is: 3×0 = 0Nm
- Moment of the 4N force about A is: 4×4=16Nm anti-clockwise (ACW) so -16Nm
- Moment of the 5N force about A is: 5×6=30 Nm CW so +30Nm

The Total Moment about point A = -16+30 = +14Nm (CW)

Keep an eye out for our next articles looking into how fluids and heat can affect engineering problems.

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