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# The Principle of Moments

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## The Principle of Moments

* Factors affecting moments*.

**Moment:** Component of force perpendicular to the door multiplied by its distance from the pivot.

When you push a door closed, it doesn't travel in a straight line - it **turns** around the hinges. This is an example of a **moment (or torque).**

Try closing a door by pushing it at the handle.

Now try closing the door by pushing it in the same way but right next to the hinges. You need more force!

And if you push the door **on** the hinge or **into** the hinge you get no turning effect at all. The door just pushes straight back and refuses to budge.

**So there are three things that are important:**

- The size of the force.
- The direction of the force.
- The distance from the force to the hinge.

**''A moment is defined as a force multiplied by the perpendicular distance from the line of action of the force to the pivot.''**

**Units:** Nm. Symbol, M (or sometimes T)

Suddenly it doesn't seem so obvious. We need a diagram to make it clear.

This one's easy. The line of action of the force is shown as a dotted line. It is already perpendicular to the door, so the distance we want is the length of the door.

Not so easy. The angle between the force and the door is **not** a right angle. So what can you do?

Well there are two ways to solve this:

**Either**, find the component of the force perpendicular to the door - for instance, F sin 30.

**Or**, find the perpendicular distance to F - for example, the **line of action** of the force is shown as a dotted line. There is only one place that you can draw a line through the hinge that will hit the line of action of the force at 90 degrees - and that is where I've drawn it as 'd'. So that's the distance we want.

**How do you find 'd'?**

Trigonometry and knowledge of angles in a triangle. Look!...

* A tricky example:*.

**What's the moment (torque) due to this force?**

Answer = **zero**! There will be no turning effect. Try it! Why is this so? Because F is not perpendicular to the door, instead it is trying to push the door straight **into** its hinges rather than **around** the hinges. The line of action of the F goes through the hinge. So the distance between the line of action and the hinge (see the definition above) is **zero**. Hence the moment is **zero.**

* For equilibrium: (i.e. an object is balanced and not moving or turning)*.

**The sum of the clockwise moments about a point = sum of the anticlockwise moments about that point.**

* A simple example:*.

(5x2)+(2x1) = (6x2)

12Nm = 12Nm

**So we have equilibrium!**

(* Note:* Have a look at the

**Equilibrium Learn-it**).

* Question:*.