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Moments, Levers and Gears

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Moments, Levers and Gears

Moments can be seen very often in everyday life. You may already have an intuitive notion of moments and use it to your advantage even if you are not familiar with its physical theory. For example, we apply the concept of moment when playing on a see-saw in the playground and measuring mass using an unequal arm scale. When used correctly, moments can help us leverage our force and heavy objects that we cannot move alone. The famous Greek mathematician and philosopher Archimedes was so excited to apply moments this way that he said, 'give me a place to stand, and I shall move the world!' Maybe you have seen people balancing objects in a way that seems to defy gravity, like those slanted bottle holders. Yes, this is another application of the concept of moments!

Moments, Levers and Gears a slated piece of wood balancing a bottle of wine StudySmarterThe bottle is balancing without effort thanks to clever use of moments in the bottle holder design, StudySmarter Originals

What is the meaning of moment in physics?

When we apply a force to an object in a certain direction, we can make it rotate. The point around which the rotation occurs is called the pivot point. Moments are all about understanding and quantifying the effectivity of a force to make an object turn.

Moment is the name we give in physics to the turning effect of a force that causes an object to rotate about a pivot.

To quantify the moment of a force,,we multiply the applied force, by the perpendicular distance of the line of action of the force from the pivot point,.

Since the units of force are newtons and units of distance are metres, we measure moment in newton-metres.

The following picture shows how to generate a moment in a nut using an adjustable wrench by applying a force in the correct direction. In this case, the centre of the nut is the pivot point.

Moments, Levers and Gears moment of  an adjustable wrench applying a force to a nut StudySmarterThe force applied to the wrench causes a moment that makes the nut turn around its centre, StudySmarter Originals

As an experiment, try opening a door by pushing it at different distances from the hinge. You will find that the further away from the hinge you push, the easier it will be to move the door. You need less force when you are farther from the hinge because you increase the perpendicular distance from the line of action of the force - your push - to the pivot - the hinge. Thus, the moment becomes greater, making the turning effect on the door more efficient.

A set of masses with a total weight ofis placed on a beam that is balanced on a fulcrum, as shown in the diagram below. This set is placed at a distance offrom the pivot. What is the moment due to the set of masses?

Moments, Levers and Gears Weights causing a moment StudySmarterA set of weights on a beam over a fulcrum causes a moment. GCSE

For this question, we need to use the equation for the moment above presented:

The applied force is the weight of the set,. Since the weight acts downwards, the given distance is perpendicular to the line of action of the weight,. Both quantities are already in SI units, so we can use the equation directly to find the moment.

The moment created by the set of masses is.

Causes of moments

From the definition provided previously, we know that force cause moment. But not just any force! For example, note that if the line of action of a force passes through the pivot, there will be no moment, as the perpendicular distance is zero. Hence, there is no rotation in such a case.

Moments, Levers and Gears an adjustable wrench applying a force to a nut generating no moment StudySmarterThe line of action of the force passes through the pivot point. In this case, the wrench does not make the nut turn as there is no moment. StudySmarter Originals

Using this idea, we can balance objects so that they do not fall. We just need to make sure that their weight - which is directed downwards - is acting in a direction that passes through the point of support of the structure that we are trying to balance - the pivot. Do you remember the definition of the centre of mass?

The centre of mass is a point where we can consider that all the mass of an object is concentrated. Its location depends on the mass distribution of an object.

Balancing an object is easy if we know where the centre of mass is. Consider the bottle shown at the beginning. If the bottle is inclined, its centre of mass does not align with the support point. Therefore, its weight will act at a certain perpendicular distance from the pivot, creating a moment. This moment makes the bottle turn towards the surface it is on, and it falls.

Moments, Levers and Gears inclined bottle showing its centre of mass StudySmarterThe weight of the bottle generates a moment because the centre of mass is not aligned to the pivot point. StudySmarter Originals

However, the slanted bottle holder is designed so that the centre of mass of the bottle holder-bottle system is directly above the support point. This way, the weight of the system does not generate a moment.

Moments, Levers and Gears slanted bottle holder showing the system's centre of mass StudySmarterThe centre of mass of a bottle holder-bottle system is aligned with the pivot point. Therefore, the system is not subject to any moment because of its weight. StudySmarter Originals

You can try this at home. If you have two identical forks, two toothpicks, and a salt shaker, you can balance the forks in a surprising way. First, interlock the forks' tines, as shown in the image below.

Moments, Levers and Gears interlocked forks StudySmarter

Interlocking the forks' tines, StudySmarter originals

Now, insert a toothpick through one of the slots in the interlocked forks until it is firm. If done correctly, you will have a structure with its centre of mass located in the vertical line passing through the non-inserted end of the toothpick. Because of this, you should be able to balance the whole structure on one of your fingers from the non-inserted end of the toothpick.

Moments, Levers and Gears a hand balancing two forks on a toothpick StudySmarterThe structure is easily balanced from the non-inserted end of the toothpick because the location of the centre of mass is right below it. StudySmarter Originals

But we can do better! Secure the second toothpick in one of the salt shaker's holes. Carefully balance the forks-toothpick structure on the second toothpick instead of your finger. This setup will work and balance because the centre of mass of the forks' system is aligned to the vertical toothpick, generating no moment to make the forks fall.

Moments, Levers and Gears two forks balanced on a toothpick's end StudySmarterSince the structure's weight acts in a line that passes through the pivot point - the second toothpick end - there is no moment to make the forks fall.

Principle of Moments

We now know that moments can cause an object to rotate, but as in the previous examples, sometimes we may prefer our system to remain static. Consider the structures lifted during construction. It is very important that these structures are not swinging around because it would be too dangerous. However, we can not always balance objects using their centre of mass. In cases like those, we need to balance the moments, and the principle of moments can help us with that.

The principle of moments states that a system is balanced if the sum of clockwise moments equals the sum of anti-clockwise moments.

An object will only rotate if there is an imbalance of moments in the clockwise and anti-clockwise directions. Therefore, we can prevent an undesired moment from causing a rotation clockwise by balancing it using an anti-clockwise moment of the same magnitude.

When a system is balanced, it is said to be in equilibrium. An example of this is when two people of the same mass sit on either side of a see-saw. Since their weights are equal, so are the distances from the pivot at the centre to either force. The generated moments are equal because of the equal forces - same weights - and perpendicular distances to the pivot. Therefore, the turning effects from the two forces cancel each other out, and the see-saw does not rotate. Note that there is also a reaction force at the pivot (represented asin the diagram below). However, this does not cause any moment because the perpendicular distance for it is zero.

Moments, Levers and Gears See-saw moments diagram StudySmarterThe moments due to either child on a see-saw depend on their masses and their distances from the pivot, philschatz

Two children are sitting on either side of a see-saw. The system is in equilibrium and is not moving. The moment applied to the see-saw by the child on the left-hand side is. The mass of the child on the right-hand side is. What is the total length of the see-saw?

We can presume that the see-saw is horizontal, and the forces acting due to the children's weights are perpendicular to it because they are directed downwards. The equation for the moment due to a force is given by:


where F is the force in newtonsandis the perpendicular distance of the line of action of the force from the pivot in metres. We can rearrange this expression to isolate the distance from the pivot:


We need to calculate the child's weight on the right, as the system is in equilibrium so it will cause the same moment as the child on the left. The force due to the child's weight is:


taking g to be is:

Now we can substitute this result in the equation for the distance.


However, we must be careful. The question asks for the length of the see-saw. This length is twice the distance from the pivot to either of the children and so it is.

More examples and applications of moments: levers and gears

With the examples discussed, you might have already started to realize how often moments are present in everyday life. Some other applications of moments include scissors and cutting pliers, which we can use to cut even through metal with just our hands' strength. Another example is removing a nail using a hammer's head and pushing or pulling the hammer's grip. The example of the hammer and nail is illustrated below. Remember that we have to consider the perpendicular distance from the pivot to the line of action of the force, not the distance from the pivot to where the force is applied.

Moments, Levers and Gears a hammer removing a nail StudySmarterA hammer removing a nail is an application of moments, StudySmarter Originals

All these particular applications of moments are known as levers. Let's see how they work in more detail.

What is a lever and how does it work?

A lever consists of a rigid bar or beam resting on a pivot (also called a fulcrum).

We can use levers to lift heavy weights more easily. Levers work on the principle that we can produce a greater moment (and thus a larger turning effect) by applying a smaller force at a greater distance from the pivot. The idea is for the fulcrum to be closer to the load - the weight that we want to lift - than it is from the point where we exert the force or effort. Have a look at the picture below. In this case, the load is a big rock. The rock's weight generates a moment on the lever system. However, we can create a moment equal or greater using less force because the distance where the effort is applied is greater.

Moments, Levers and Gears a lever being used to lift a heavy weight StudySmarter A lever uses moments to lift a heavy weight. The load to be lifted causes a moment. However, we can cause a greater moment by applying less force than the weight of the load if we apply it at a larger distance from the fulcrum. StudySmarter Originals

A wheelbarrow is another example of the applications of levers. Loads that are too heavy to carry directly can be transported using wheelbarrows instead. The load is placed at the bottom above a wheel, and two handlebars come up it. These handlebars can be lifted using less force than the load itself as the effort is applied further from the pivot than the load is.

Moments, Levers and Gears Wheelbarrow moment diagram StudySmarterP represents the pulling force or 'effort' applied by the person, and R represents the load resistance due to its weight. The pivot is located at the centre of the wheel, tec.amordediocadiz

The diagram above shows the forces acting in this situation. Both forces act at the left of the pivot of the system, which is at the centre of the wheel. However, these forces are acting in opposite directions. The load's weight is causing an anti-clockwise moment. On the other hand, the force the person applies by pulling the handlebars - the effort - generates a clockwise moment.

We can see that levers are very useful, but they are not the only applications of moments. We also apply this concept when using gears.

What is a gear and how does it work?

Gears are toothed wheels (they have little bumps surrounding their edge) such that they can interlock together.

You may have seen gears in various places, such as bicycles and pulleys. Gears, yet simple, can be very useful since they have different applications. For example, when gears are connected to each other, they can turn at different rates because for a bigger gear to complete a turn, a smaller gear needs to complete more turns. The exact amount of turns depends on the gears' sizes. Note that if one gear is spinning anti-clockwise, this causes the connected gear to rotate clockwise. Therefore, we can use them to change the direction in which an object is spinning as well.

Moments, Levers and Gears Gears diagram StudySmarterIf one gear turns in one direction, this will result in the other turning in the opposite direction, Wikimedia commons

But how exactly is the concept of moment applied here? At the point of contact for the gears' teeth, a force equal and opposite is exerted on each other. However, as their radii are different, the moments acting on either gear are also different. Applying a force to the smaller gear will cause a greater moment on the bigger gear because the force applied to it will be the same, but its radius is greater.

Key takeaways

  • A moment is the turning effect of a force that causes an object to rotate about a pivot.

  • We calculate the moment of a force by multiplying the applied force by the perpendicular distance from the pivot to the line of action of the force.

  • The principle of moments states that when a system is in equilibrium, the sum of the clockwise moments equals the sum of anti-clockwise moments about the pivot.

  • A force acting directly through the pivot of a system will produce no moment about the pivot.

  • Levers use moments to advantage and can be used to increase the moment to turn something or lift a heavy object.

  • Different sizes of gears can be connected to increase or decrease the magnitude of a moment.

Frequently Asked Questions about Moments, Levers and Gears

A moments is the turning effect of a force that causes an object to rotate about a pivot. A lever rigid bar resting on a pivot that helps to turn something by increasing the moment acting on it.

The moment due to a lever can be found by multiplying the force applied by the perpendicular distance of the line of action of the force from the pivot.

Gears are toothed wheels that interlock and cause different sized moments due to their different radii.

Levers reduce the force needed to apply the same moment as they increase the perpendicular distance from the line of action of the force to the pivot.

For interlocked gears, the gear with the larger radius will have the larger moment.

Final Moments, Levers and Gears Quiz


What is a moment?

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A moment is the turning effect of a force.

Show question


A force acting directly through the pivot of a system produces no moment. Is this true or false?

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Show question


What is the principle of moments?

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When a system is in equilibrium, the sum of the clockwise moments equals the sum of anticlockwise moments.

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Give an example of when moments are used in everyday life.

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For example: spanners, door handles, see-saws etc

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Give an example of a lever.

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eg a pair of scissors, a door handle

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Will a larger or smaller gear complete a turn faster?

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A smaller gear

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Which of the following is an example of a use of gears

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If two differently sized gears are connected, which one has a greater moment?

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The larger gear as the force applied is the same for both, but the radius is greater for the larger one.

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Why is the effort force used to lift a load with a wheelbarrow less than lifting the load without it? 

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Because the same moment can be applied with less force if the force is applied further away from the pivot. 

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What is a pivot?

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A fixed point around which a system can rotate.

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A moment of 0.2 Nm needs to be applied to a door handle to be able to open the door. If the length of the door handle is 0.1 m, what force must be applied?

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2 N

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A 20 kg child sits on the right-hand side of a see-saw at 1.5m from the centre. At what distance must a 30 kg child sit on the opposite side to balance the see-saw? 

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1 m

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A person lifts a wheelbarrow by applying a force of 20 N. If the distance of the handlebars from the wheels is 1.5 m, what is the moment? 

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30 Nm

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