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Wheel and Axle in Simple Machines: Definition, Formula, and Calculations

What is Wheel and Axle in Simple Machines?

Wheel and Axle Definition: A wheel and axle is a simple machine consisting of a circular wheel attached to a central axle. It allows for the efficient transfer of force to accomplish tasks like lifting.

The invention of the wheel and axle dates back to ancient times, and it’s challenging to assign it to a single person. Early human societies developed this simple machine to make tasks like transportation and manufacturing easier. The wheel and axle were innovations that emerged independently in different cultures, marking a significant step in human technological progress.

Additionally, the wheel and axle is a basic mechanical device that consists of two components: a circular object known as the wheel and a shaft called the axle. These components are joined together in such a way that the wheel rotates around the axle.

This arrangement enables the transfer of force and motion between the two components, making it a very important tool in the field of mechanics.

How Does a Wheel and Axle Make Work Easier

We will now explain the working principle behind the wheel and axle, which is a cool machine that makes tasks easier. Imagine you have a doorknob or a steering wheel – those are examples of a wheel and axle!

Wheel and Axle:
A wheel and axle is like a tag team where one helps the other do the work. It is made up of a round wheel and a rod-like axle sticking through the centre. The wheel is the circular part you hold onto, like the steering wheel on a bike, and the axle is the rod in the middle.

How it Works:
A wheel and axle make work easier by leveraging the principle of mechanical advantage. When you turn the wheel, it rotates the axle, and the sizes of the wheel and axle determine the mechanical advantage. A larger wheel compared to the axle means less effort is needed to turn it. This design helps distribute force effectively, making it easier to perform tasks like turning, lifting, or moving objects. Moreover, the wheel and axle work together, allowing us to use less force to achieve more significant effects, making various activities in our daily lives more manageable.

Imagine you have a bike. When you turn the handlebars (which is like turning a wheel), the whole wheel turns along with the axle. That is the magic of the wheel and axle – when you spin one part, the other spins too!

Making Things Easier:
Think about a doorknob. Turning the small knob spins the big wheel, making it easier for you to open the door. It is like teamwork between the wheel and axle, so you don’t have to push the whole door.

Everyday Examples:
Apart from bikes and doorknobs, think about a screwdriver. The handle is like the wheel, and the screw is the axle. When you twist the handle, it makes turning the screw much easier.

Key Idea:
So, the wheel and axle make tasks simpler by letting you use less force to get things done. It’s like having a buddy that helps you out when you want to turn, twist, or spin something!


To fully understand the mechanics behind the wheel and axle, we need to have a picture of the concept of torque. Torque is the twisting force that causes an object to rotate around an axis. In the case of the wheel and axle, when a force is applied to the wheel, it generates torque, causing the axle to rotate.

Wheel and Axle Examples

Here are 20 examples of wheel and axle around you:

  1. Bicycle: The wheels and pedals form a wheel and axle system.
  2. Car Wheels: The rotation of the wheel is facilitated by the axle.
  3. Steering Wheel: In a vehicle, turning the wheel turns the axle, allowing directional control.
  4. Doorknob: Rotating the knob turns the latch through a wheel and axle mechanism.
  5. Rollerblades: The wheels on rollerblades spin on axles.
  6. Shopping Cart Wheels: The wheels on a shopping cart rotate around axles.
  7. Ferris Wheel: The large circular structure rotates around a central axle.
  8. Hand Mixer: The beaters spin around an axle when powered on.
  9. Grinding Wheel: Used in tools, the wheel rotates around an axle.
  10. Record Player: The turntable rotates on an axle to play vinyl records.
  11. Pulley System: A system with multiple wheels and axles for lifting loads.
  12. Fishing Reel: The spool, acting as a wheel, rotates on an axle.
  13. Hand Drill: Turning the handle rotates the drill bit through a wheel and axle.
  14. Crankshaft in Engines: Converts linear motion into rotational motion.
  15. Water Wheel: Used historically for various mechanical tasks.
  16. Clock Mechanism: The hands rotate around axles to indicate time.
  17. Gears in Machinery: Many gear systems utilize the wheel and axle concept.
  18. Tape Dispenser: The tape roll rotates on an axle for easy dispensing.
  19. Wagon Wheels: Classic examples of large wheels mounted on axles.
  20. Potter’s Wheel: Used for shaping clay, the wheel rotates on an axle.

Applications of Wheel and Axle

The wheel and axle find applications in different fields, contributing significantly to human progress and convenience. Some of the most notable applications include:

  1. Transportation: From ancient carts to modern automobiles, the wheel and axle have revolutionized transportation, making it faster and more efficient.
  2. Machinery: Many machines and equipment, such as pulleys, windmills, and gears, rely on the wheel and axle for their operation.
  3. Lifting Devices: Cranes and lifting machines utilize the mechanical advantage of the wheel and axle to lift heavy loads with ease.
  4. Vehicles: The wheels of bicycles, motorcycles, and aeroplanes are classic examples of the wheel and axle at work.

The Formula and Calculations of Wheel and Axle

To understand the principles of the wheel and axle more deeply, we need to explore the fundamental formula that governs its behavior.

Wheel and Axle Formula

The mechanical advantage (MA) of the wheel and axle is a crucial aspect that determines its efficiency in transferring force. The formula for calculating the mechanical advantage is as follows:

MA = Rwheel / Raxle

We can equally use: MA = V.R = R/r


  • MA is the mechanical advantage.
  • V.R is the velocity ratio.
  • Rwheel or R is the radius of the wheel.
  • Raxle or r is the radius of the axle.

Understanding the Mechanical Advantage

The mechanical advantage indicates the multiplication of force achieved by the wheel and axle. When the radius of the wheel is greater than that of the axle, the mechanical advantage becomes greater than 1. This implies that the force applied to the wheel is amplified, making it easier to lift or move heavy objects.

Conversely, if the radius of the axle is greater, the mechanical advantage is less than 1. In such cases, the wheel and axle act as a speed multiplier, meaning the wheel rotates faster than the force applied to it.

Solved Problems

Problem 1

Calculate the mechanical advantage of a wheel with a radius of 20 centimetres and an axle with a radius of 5 centimetres.

Using the formula, we can calculate the mechanical advantage:

MA = Rwheel / Raxle = R/r

Thus, MA = R/r

Where; R = 20cm, and r = 5cm

Substituting our formula with the above data, we will now obtain:

MA = (20 cm) / (5 cm) = 4

Therefore, the mechanical advantage (MA) of the wheel and axle is four (4). Remember that your final answer for wheel and axle does not have a unit. Additionally, we have seen that the wheel and axle in this example provide a mechanical advantage of 4, which indicates that the force applied to the wheel is four times greater than the force applied to the axle.

Problem 2

A wheel and axle are used to raise a weight of 240 kg. The radius of the wheel is 50 cm, and axle is 10 cm. When a force of 75 kg is applied on the wheel, the weight is raised with a uniform velocity. Find the mechanical advantage and the velocity ratio.


Data: The information available from the question.

Load (L ) = Weight (W) = 240 kg, Radius of the wheel (R) = 50 cm, Radius of the axle = 10 cm, Applied force or effort (E) = 75 kg.

Formula: The equation from the question.

The mechanical advantage, MA = L/E

Velocity ratio, VR = R/r

Solving the Problem

The mechanical advantage, MA = L/E = 240 kg / 75 kg = 3.2

Velocity ratio, VR = R/r = 50/10 = 5

Therefore, the mechanical advantage (MA) is 3.2 while velocity ratio (VR) is 5.

How to Maximize Efficiency with the Wheel and Axle

To ensure optimal performance and efficiency when using the wheel and axle, there are some essential considerations to keep in mind.

a. Choosing the Right Materials

You need to select an appropriate material for the wheel and axle, especially when dealing with heavy loads or high-speed applications. Durable and friction-resistant materials can enhance the machine’s lifespan and reduce energy loss.

b. Proper Lubrication

Applying the right lubrication between the wheel and axle minimizes friction, allowing for smooth rotation and improved efficiency.

c. Balancing the Wheel

A balanced wheel ensures an even distribution of weight, reducing vibrations and wobbling during operation.

d. Regular Maintenance

Regular inspection and maintenance of the wheel and axle prevent unexpected breakdowns and ensure optimal performance.


Q: What are the primary components of the wheel and axle?
The wheel and axle consist of two key components: the wheel, which is a circular object, and the axle, a shaft that the wheel rotates around.

Q: How does the wheel and axle function?
When a force is applied to the wheel, it generates torque, causing the axle to rotate, resulting in the transfer of motion.

Q: What is the formula for calculating the mechanical advantage of the wheel and axle?
The formula is MA = (Radius of Wheel) / (Radius of Axle).

Q: What is the significance of the mechanical advantage?
The mechanical advantage determines the amplification of force achieved by the wheel and axle, making it easier to lift heavy loads or increase rotational speed.

Q: What are the applications of the wheel and axle?
The wheel and axle are used in transportation, machinery, lifting devices, and various vehicles.

Q: How can I maximize efficiency when using the wheel and axle?
Efficiency can be maximized by choosing the right materials, applying proper lubrication, balancing the wheel, and conducting regular maintenance.

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