What are the key learning points about moments?
The moment of a force about a A point around which something can rotate or turn. is the product of the force and the The distance from the pivot which makes a right angle with the line of action of the force. A pivot is a point around which something can rotate or turn. to the pivot.
If the distance is in cm, then the moment is in Ncm; if the distance is in metres then the moment is in Nm. Moments have a direction — they are either clockwise or anticlockwise.
The principle of moments states that: When an object is balanced, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point.
The centre of gravity of an object is the point where all of the weight of the object can be considered as acting.
Objects with a wide base, and a low centre of gravity, are more stable than those with a narrow base and a high centre of gravity.
What is the turning effect?
A force may cause an object to turn about a A point around which something can rotate or turn. .
The turning effect of a force is called the moment of the force.
Moments act about a pivot in a clockwise or anticlockwise direction.
The moment of a force is a A physical quantity that has magnitude (size) and direction. Examples: displacement, velocity, acceleration, force, weight. quantity.
The direction of the moment is either clockwise or anticlockwise.
Definition of a moment: A moment is defined as the product of the force and the perpendicular distance from the force to the pivot.
What are examples of the application of moments in everyday life?
Some examples of the application of moments are:
- Placing the door handle far away from the hinge means less force is needed to open a door.
- It is easier to loosen a nut with a long spanner than a short one because the force can be applied further away from the pivot so less force is needed to create the same moment.
What are levers?
Removing the lid from a can of paint requires a large lifting force on the lid.
A screwdriver acts as a lever.
The pivot is the edge of the can and this is very close to where the strong push is needed to lift the lid to open the can.
A screwdriver with a long handle means that you can push down on the handle of the screwdriver with a small force and still open the can.
How to calculate the moment of a force
The size of the The moment of a force is the turning effect of the force. Moment = force x perpendicular distance from the pivot. can be calculated using the equation:
moment of a force = force F x perpendicular distance from the pivot d
moment = F x d
Force F is measured in Unit of force named after British scientist Isaac Newton (1642-1727). Eg, the frictional force on the boat is 20,000 N.
Distance d is measured in metres (m) or in centimetres (cm).
Moment is measured in newton metres (Nm) or (if d is in centimetres) newton centimetres (Ncm).
The turning effect or moment of a force depends on two factors:
The size of the force.
The perpendicular distance the force is from the pivot.
The distance from the pivot which makes a right angle with the line of action of the force. A pivot is a point around which something can rotate or turn. from pivot to force d = 0.50 m.
Force F = 10 N
Moment = Fd
Moment = 10 N x 0.50 m
Moment = 5 Nm
This is a clockwise moment.
The force will rotate the object in a clockwise direction about the pivot.
Key fact
The distance d is the perpendicular distance from the pivot to the line of action of the force (see diagram).
Question
A force of 15 N is applied to a door handle, 12 cm from the hinge.
Calculate the moment of the force.
Answer
Perpendicular distance from pivot to force d = 12 cm = 0.12 m.
Turning force F = 15 N.
Moment = Fd.
Moment = 15 N x 0.12 m.
Moment = 1.8 Nm.
The moment of the force is 1.8 Nm.
Question
A force of 40 N is applied to a spanner to turn a nut.
The perpendicular distance is 30 cm.
Calculate the moment of the force.
Answer
Perpendicular distance from pivot to force d = 30 cm = 0.30 m.
Turning force F = 40 N.
Moment = Fd.
Moment = 40 N x 0.30 m.
Moment = 12 Nm.
The moment is 12 Nm. This is a clockwise moment.
Learn more about moments and levers
A moment is the turning effect of a force around a fixed point, the pivot. Examples include a door opening around a fixed hinge, seesaws, scissors or a spanner turning around a nut.
Moments are measured in Newton metres and the size of a moment depends on two factors: the size of the force applied and theperpendicular or right-angle distance from the pivot to the line of action of the force.
We can calculate the moment of a force using the equation:
Moment equals Force multiplied by the Perpendicular Distance to the Pivot.
Let's look at a practical example.
A lever is a rigid body that rotates about a pivot or fulcrum.
A spanner is an example of a lever.
If we apply a 25 Newton force to the end of the 10-centimetre-long spanner to turn a nut, what is the moment?
We work this out by multiplying the distance from the pivot to the point on the spanner where the force is applied in metres by the force on the spanner.
So that's 0.1 metres multiplied by 25 Newtons, which is 2.5 Newton metres.
But what if that's not enough to undo the nut?
Well, we can just use a longer spanner.
Let's increase the length of the spanner to 20 centimetres, keeping the force used at the end of the spanner at 25 Newtons.
Using the same equation, we would produce a moment of 5 Newton metres on the nut.
Sometimes objects can experience more than one moment.
These moments can combine to make a bigger turning effect or can work against each other to reduce the turning effect. In a stable or balanced system, the anticlockwise moments are equal to the clockwise moments.
A seesaw is a balanced system of moments where two people are balanced on a solid object on top of a fulcrum or pivot.
Since the system is balanced, we can calculate an object's weight measured as a downward force in Newtons, or distance from the pivot.
If two people (Person A and Person B) sit on a seesaw, the moment of each person equals their weight multiplied by their distance from the pivot.
When balanced, these moments are equal.
So, the moment of Person A, their weight multiplied by their distance from the pivot equals the moment of Person B, their weight multiplied by their distance from the pivot.
Using and rearranging this equation, we can always work out a value for one of the values of weight or distance if we know the other three values.
Prescribed practical P3: The principle of moments
A guide to carrying out an experiment to determine the principle of moments
What is the purpose of prescribed practical P3?
To plan and carry out experiments to verify the principle of moments using a suspended metre rule and attached weights.
The principle of moments states that when an object is balanced, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point.
What equation is used to calculate the moment of a force?
Moment = force F x perpendicular distance from the pivot d.
Moment = F x d
What apparatus is used in an experiment to verify the principle of moments?
A A uniform object is one that exhibits consistent or identical characteristics across its entire structure. For example, a meter rule, made of the same material throughout, with equal thickness and weight along its length is a uniform object. This evenness ensures accurate measurements. metre rule, retort stand, boss and clamp, two 100 g mass hangers and 12, 100g slotted masses, a g-clamp, three lengths of string.
What method is used to carry out prescribed practical P3?
- Suspend the metre rule at the 50 cm mark so that it is balanced horizontally. The ruler is said to be in equilibrium. The 50 cm mark is the pivot.
- Suspend a mass, m1, from one side of the ruler a distance, d1, from the pivot. Read the distance d1 in cm, from m1 to the pivot. Record in a suitable table. Record the value of mass m1 in kg in the table too.
- Suspend a second mass, m2, from the other side of the pivot. Carefully move this mass backwards and forwards until the ruler is once more balanced horizontally. Read the distance d2 in cm from the mass m2 to the pivot. Record d2 in cm, in the table, along with the mass m2 in kg.
- Repeat several times using different masses and distances.
- Calculate the turning forces, F1 and F2, using W = mg.
- Calculate the clockwise and anticlockwise moments.
Safety
Clamp the retort stand to the bench with the g-clamp so it doesn’t fall and hurt someone or fall on their feet.
Place an obstacle, such as a stool, to keep feet from beneath the metre rule, to make sure the mass hangers don’t fall on someone’s foot.
Safety glasses should be worn in case the meter rule swings and hits someone in the eye.
Results
For ANTICLOCKWISE moment:
| Mass m1 / kg | Turning force F1 / N | Perpendicular distance from the pivot d1 / cm | Anti- clockwise Moment / Ncm |
|---|---|---|---|
For CLOCKWISE moment:
| Mass m2 / kg | Turning force F2 / N | Perpendicular distance from the pivot d2 / cm | Clockwise Moment / Ncm |
|---|---|---|---|
Conclusion
Each time the ruler balances horizontally, the results recorded in the table will show: the anticlockwise moment about the pivot = the clockwise moment about the pivot.
This then verifies the Principal of Moments.
What is the principle of moments?
When an object is balanced, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point
This is called the principle of moments.
Total clockwise moment = Total anticlockwise moment.
Question
The diagram below shows two masses balanced on a level beam.
Question
How far is the 10 N weight from the pivot?
Answer
The beam is balanced and so from the principle of moments we know that:
Total clockwise moment about the pivot = Total anticlockwise moment about the pivot.
Calculate each individual moment first:
Anticlockwise moment
The distance from the pivot which makes a right angle with the line of action of the force.from the pivot = d m.
Force F = 10 N.
Anticlockwise moment = F x d = 10 N x d m = 10d Nm.
Clockwise moment
Perpendicular distance from the pivot = 1 m.
Force F = 20 N.
Clockwise moment = F x d = 20 N x 1 m = 20 Nm.
Total clockwise moment = Total anticlockwise moment
10d = 20.
\({d}=20~Nm~÷~10~N\)
d = 2 m
The 20 N weight is 2 m from the pivot.
Question
A parent and child are at opposite sides of a playground see-saw.
The parent sits 0.8 m from the pivot.
The child sits 2.4 m from the pivot and weighs 250 N.
Calculate the weight of the parent if the see-saw is balanced.
Answer
The see-saw is balanced and so from the principle of moments we know that:
total clockwise moment about the pivot = total anticlockwise moment about the pivot.
Anticlockwise moment
The anticlockwise moment is the child's moment = Fd.
Perpendicular distance of child from the pivot = 2.4 m.
Force F = 250 N.
Anticlockwise moment = 250 N × 2.4 m = 600 Nm.
Clockwise moment
The clockwise moment is the parent's moment = Fd.
Perpendicular distance of adult from the pivot = 0.8 m.
Force F = F N.
Clockwise moment = F N x 0.8 m = 0.8F Nm.
Total clockwise moment = Total anticlockwise moment
0.8 F = 600.
F = 600 Nm ÷ 0.8 m.
F = 750 N.
The parent’s weight equals 750 N.
Determine the weight of a uniform ruler using the principle of moments
The clockwise moment is provided by the weight of the ruler which acts vertically downwards from the The centre of an object from which the force of gravity acts. at the 50 cm mark.
The anticlockwise moment is provided by the known weight.
If we apply the principle of moments about the pivot, we see that:
Total clockwise moments = Total anticlockwise moments
W2 × d2 = W1 × d1
where W1 is the known weight and d1 is the distance from the pivot to the known weight, W2 is the weight of the ruler and d2 is the distance from the pivot to the 50cm mark.
Hence, weight of the ruler = (W1 × d1)/d2
Repeat the experiment using different known masses, and different values of d1.
Record the results in a suitably headed table and calculate an average value for the weight of the ruler.
What is the centre of gravity?
Key facts
The centre of gravity is the point through which the entire weight of a body appears to act.
The weight of an object acts vertically downwards from the centre of gravity.
Where is the centre of gravity on an object?
Depending on the shape of the object, its centre of gravity can be inside or outside it.
Regular shapes
A metre rule is a A uniform object is one that exhibits consistent or identical characteristics across its entire structure. For example, a meter rule, made of the same material throughout, with equal thickness and weight along its length is a uniform object. This evenness ensures accurate measurements. and regular shape, therefore its centre of gravity, G, is at its centre ie at the 50 cm mark.
The metre rule balances freely at its centre of gravity.
What is stability?
Stability is a measure of how likely it is for an object to topple over when pushed or moved.
Stable objects are very difficult to topple over, while unstable objects topple over very easily.
Key fact
An object will topple over if its centre of gravity is ‘outside’ the base, or edge, on which it balances.
The yellow car has a wider wheel base and lower centre of gravity than the blue car.
It is more stable.
The wheel acts as the A point around which something can rotate or turn. for the car.
The weight has a turning effect or moment, which causes the car to topple over or fall back.
Key fact
For an object to be stable it must have:
- A wide base.
- A low centre of gravity.
Objects with a wide base, and a low centre of gravity, are more stable than those with a narrow base and a high centre of gravity.
A double decker bus is stable as it has a:
- Low centre of gravity because of its low, heavy engine and heavy bottom deck.
- Wide wheel base.
A traffic cone is stable as it has a:
- Low centre of gravity G because of its heavy base.
- A wide base.
Question
The diagram below shows a bus in two positions.
The centre of gravity of the bus is marked with a G.
For each position describe and explain what happens to the bus.
Answer
Position 1
- The bus does not topple over.
- This is because the centre of gravity G is inside the wheel base. The weight produces a clockwise moment about the pivot, pulling the bus back onto its base.
Position 2
- The bus topples over.
- This is because the centre of gravity G is outside the wheel base. The weight produces an anticlockwise moment about the pivot, pulling the bus off its base and on to its side.
Can you find the centre of gravity?
Test your knowledge
More on Unit 1: Forces
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