Moments, Levers and Gears

Moments are a part of our everyday life. Even if you don't know the physical theory behind it, you probably use moments without realizing it. For example, when you play on a see-saw or use an unequal arm scale to measure mass. Moments can help you move heavy objects by leveraging your force. Archimedes, a famous Greek mathematician and philosopher, was so excited about this concept that he once said, "give me a place to stand, and I shall move the world!" You may have seen people balancing objects in a way that seems impossible, like those slanted bottle holders. This is another application of the concept of moments. So, next time you see a see-saw or a slanted bottle holder, think about the levers and gears at work!

Just keep reading if you want to learn the details behind all these applications and balance your own gravity-defying structure using everyday things!

What is the meaning of moment in physics?

We can make an object rotate by applying a force in a certain direction. The point where the rotation occurs is called the pivot point. Moments are all about understanding how effective a force is in making an object turn. Moment is the name we use in physics for the turning effect of a force that causes an object to rotate around a pivot. To calculate the moment of a force, we multiply the applied force by the distance between the pivot point and the line of action of the force. We measure moment in newton-metres because force is measured in newtons and distance is measured in metres. The picture below shows how to generate a moment in a nut using an adjustable wrench by applying force in the correct direction. In this case, the pivot point is the centre of the nut.

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?

A 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.

The idea of using moments to balance objects is very useful. To balance an object, we need to make sure that its weight is acting in a direction that passes through the point of support - the pivot. The location of the centre of mass is crucial for balancing an object. The centre of mass is a point where we can consider that all the mass of an object is concentrated, and its location depends on the mass distribution of the object. If an object, like the bottle in the example, is inclined, its centre of mass does not align with the support point. As a result, its weight will act at a certain perpendicular distance from the pivot, creating a moment. This moment causes the object to turn towards the surface it is on, and it falls.

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.

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.

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.

That's idea! holes and balancing the forks-toothpick structure on the second toothpick, we can achieve a stable balance. This is because the centre of mass of the forks' system is aligned with the vertical toothpick, and there is no moment that could make the forks fall. Since 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. This is a great example of how understanding the concept of moments and centre of mass can help us achieve stable balance.

Principle of Moments

The principle of moments is an important concept that helps us balance objects and structures. It states that a system is balanced if the sum of clockwise moments equals the sum of anti-clockwise moments. By balancing moments, we can prevent undesired rotations and achieve equilibrium. An example of this is when two people of the same mass sit on either side of see-saw. Since their weights are equal and the distances from the pivot at the centre to either force are the same, the generated moments are equal and cancel each other out, keeping the see-saw in equilibrium.

Moments are present in many everyday applications, such as scissors and cutting pliers, where we can use them to cut through materials with just our hands' strength. Removing a nail using a hammer's head is another example that involves moments. When using a hammer, we have to consider the perpendicular distance from the pivot to the line of action of the force, not just the distance from the pivot to where the force is applied.

Understanding moments and their applications can help us tackle various problems in everyday life, from balancing structures to cutting materials and fixing things around the house.

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?

By using a lever, we can lift heavy weights with less effort. Levers work on the principle that we can produce a greater moment by applying a smaller force at a greater distance from the pivot. The pivot, also called the fulcrum, is the point at which the lever is supported and around which it rotates. The idea is for the fulcrum to be closer to the load we want to lift than it is from the point where we exert the force or effort.

In the picture above, the load is a big rock, and its 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. By applying a force at the end of the lever furthest from the fulcrum, we can lift the heavy rock with less effort than we would need without the lever.

Levers are used in many everyday applications, such as lifting weights in a gym or moving heavy objects around the house. They are also used in machines and tools, such as jacks, cranes, and pliers. Understanding the principles of levers can help us work more efficiently and effectively, saving us time and effort in various tasks.

addition to levers, gears are another example of the applications of moments. Gears are used to transmit torque, which is the rotational equivalent of force. They work by meshing with each other to transmit power and motion between different parts of a machine. The teeth of the gears engage with each other, and as one gear turns, it causes the other gear to turn as well.

The principle behind gears is that they can change the speed and rotating force. By using gears of different sizes, we can increase or decrease the rotational speed of a system. The larger gear turns more slowly but with greater torque, while the smaller gear turns faster but with less torque.

Gears are used in many everyday applications, such as in cars, bicycles, and clocks. They are also used in industrial machinery, such as conveyor systems and manufacturing equipment. Understanding the principles of gears and moments can help us design and build more efficient and effective machines and systems.

What is a gear and how does it work?

In summary, gears are toothed wheels that can interlock together to transmit power and motion between different parts of a machine. By using gears of different sizes, we can increase or decrease the rotational speed of a system, and we can also change the direction in which an object is spinning.

The concept of moment is applied to gears at the point of contact for the gears' teeth, where 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.

Understanding the principles of moments and gears can help us design and build more efficient and effective machines and systems, making our lives easier and more productive.

Moments, Levers and Gears

What are moments and levers?

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.

How do you find the moment of a lever?

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.

How do gears work?

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

How do levers reduce force?

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.

What is the relationship between gears and moments?

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