Moments

The moment is the _______________ effect produced by a force about a pivot.

A moment is defined as the ________ multiplied by the ___________________ from the pivot.

Equation : moment = _______Units : _________

1.

The moment produced by the load is

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The direction is ____________________

2. Find the moment produced in the following diagram

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3. Give the value of the force F required to produce a moment of 28Nm

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If the bar/ ruler is horizontal or balanced, it means that the ruler is in equilibrium

This means that the conditions for equilibrium are met:

The principle of moments applies

The total upward forces is equal to the total downward forces.

The principle of moments states that

the total clockwise moment about a pivot is equal to the total anticlockwise moment about that pivot.

4 A uniform rod of negligible weight is pivoted at the centre.

Uniform rod means that the centre of gravity of the rod is in the middle.

negligible weight means that the weight of the rod is too small to be taken into account.

Consider the balanced rod below

Since the rod is balanced, the principle of moments apply

i) what is the anticlockwise moment?

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ii) What is the anticlockwise moment?

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iii) Give a reason for your answer to ii)

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iv) Calculate the value of F.

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. Another way of presenting the same question:

5. A rod is in equilibrium as shown below. Calculate the force F.

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Notice that for the same moment, the further the force is from the pivot, the smaller the force needed.

There can be more than 2 forces

6. The ruler is balanced as shown below:

This time we need to use the fact that the total moments will balance out.

i) What is the total clockwise moment?

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ii) What is the total anticlockwise moment? __________________________________

iii) Find F ____________________________________________________________

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Forces acting at the pivot

7. Consider the following situation. A uniform wooden plank of weight 2N is pivoted at its centre and balanced.

i) Mark and label the two missing forces.

Remember: uniform means that weight acts at the centre.

Why are these two forces not used when calculating moments?

Forces acting at the pivot _______________________________________________

When you need to find force acting at the pivot you need to use the second condition for equilibrium which states that:

The total upward forces is equal to the total downward forces.

ii) Give the value of the upward force.

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8. Mark and label the two missing forces.

If the seesaw of weight 600N is in equilibrium, find the value of the other missing force.

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Sometimes, there are two pivots ( usually called supports). This is when a plank of wood rests on two supports for example. Or a bridge rests on the sides on a bank as shown below.

9.

i) label the missing forces. Call them RA and RB.

To find these forces, we need to find them one by one.

Since forces acting at the pivot do not produce a moment, we will put the pivot underneath one of them to find the other one.

Lets put the pivot under RA. Now use moments to calculate RB.

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To find RA, we either do the same thing but this time we put the pivot under RB or else easier still we use the second condition for equilibrium.

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10. A plank of negigible weight rests on two supports as shown. A box of weight 3N is placed on the plank.

Calculate the two reaction forces.

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