Centrifugal Force – Definition, Principle, Formula, Calculation, Examples

What is Centrifugal force?

• Centrifugal force is a physics concept that occurs when an object moves in a round path. It is referred to as a fake force since it appears only in a rotating frame of reference and is not an actual force acting on the item. Instead, an apparent force occurs as a result of the object’s inertia.
• When an object moves in a circular path, it is subjected to a centripetal force directed towards the rotation’s centre. This centripetal force causes the thing to move in a curved rather than straight line. The centrifugal force, on the other hand, appears to act on the item from the outside, away from the centre of rotation and parallel to the axis of revolution.
• In a frame of reference spinning at angular velocity (), the magnitude of centrifugal force (F) experienced by an object with mass (m) at a distance (r) from the centre of rotation may be computed using the equation: F = mω²r
• The centrifugal force is proportional to the object’s mass, angular velocity squared, and distance from the centre of rotation. It is worth noting that the centrifugal force has the same magnitude and dimensions as the centripetal force but acts in the opposite direction.
• The concept of centrifugal force is used in a variety of rotating devices and systems. Centrifuge rotors, for example, use centrifugal force to separate material of varying densities. This force is used by centrifugal pumps to transport fluids from one pressure area to another. Centrifugal governors and centrifugal clutches utilise centrifugal force in their operation as well.
• Furthermore, centrifugal force is important in other contexts, such as planetary orbit analysis and banked curves. The concept of centrifugal force aids in explaining observable motion when investigating these phenomena in a rotating coordinate system.
• It is worth noting that the word “centrifugal force” can also refer to the reactive centrifugal force, which is a real inertial force that arises as a result of a centripetal force. This reactive centrifugal force is not fictional and is independent of the reference frame.
• Centripetal force, as opposed to centrifugal force, acts on an object in curvilinear motion and is directed towards the axis of rotation or the centre of curvature. It is always perpendicular to the displacement of the object and keeps it travelling in a circular route. The newton is the unit of centripetal force.
• To summarise, centrifugal force is a fictional force that occurs when a spinning frame of reference is used. It is a force felt by objects travelling in a circular route that is parallel to the axis of rotation. The magnitude of centrifugal force is determined by the object’s mass, distance from the centre of rotation, and rotational speed. It is useful in analysing systems in a rotating coordinate system and has practical applications in various rotating devices.

Definition of Centrifugal force

Centrifugal force is an outward fictitious force experienced by objects moving in a circular path, directed away from the center of rotation.

Centrifugal force formula

The centrifugal force can be calculated using different formulas depending on the available information. If the velocity (v) of the moving object is known, the formula to calculate the centrifugal force is:

Centrifugal force = m * v² / r

Here, m represents the mass of the moving object, v is its velocity, and r is the distance of the object from the center of rotation.

Alternatively, if the angular velocity (ω) of the moving object is known, the centrifugal force can be calculated using the formula:

Centrifugal force = m * ω² * r

F = mω²r

In this formula, m represents the mass of the object, ω is the angular velocity, and r is the distance of the object from the center of rotation.

These formulas allow for the calculation of the centrifugal force based on either the linear velocity or the angular velocity of the moving object, combined with the mass and distance from the center. They provide a quantitative understanding of the magnitude of the centrifugal force acting on an object in circular motion.

Principle of Centrifugal force

• The idea of centrifugal force explains the apparent outward force felt by things moving in a circle. It is vital to remember that centrifugal force is a product of inertia and its interaction with centripetal force.
• When an item, such as an automobile, turns a corner, centripetal force operates on all portions of the vehicle, causing the vehicle to change direction. However, due to inertia, the people within the car prefer to retain their straight-line motion. As a result, they appear to move out from the centre of the turning circle and towards the outer edge of their seats.
• This adjustment in the passengers’ position is produced by their own inertia rather than an external force. The passengers’ inertia opposes the change in their straight-line motion and causes them to continue going in the same direction. This provides the sense of a force pulling them towards the car’s outer edge.
• The force felt by the passengers, which appears to push them away from the car, is known as centrifugal force. However, the centrifugal force is a hypothetical force according to Newton’s principles of motion. According to Newton’s second law, acceleration is exactly proportional to the force acting on an object. Because centrifugal force does not produce acceleration on its own, it is not classified as a genuine force.
• Consider a stone that is linked to a string and revolved around a pole to further demonstrate this principle. As the stone rotates, its velocity changes direction, causing acceleration. Due to inertia, if the string breaks, the stone will tend to move in a straight line parallel to its circular path. If centrifugal force existed, the stone would travel in an outward rather than tangential direction.
• In summary, the centrifugal force theory explains the observed outward force felt by objects in circular motion. It is caused by the items’ inertia in resisting changes in their straight-line motion. Centrifugal force, despite being referred to as a force, is a fictional force because it does not induce acceleration on its own and is a result of the interplay between inertia and centripetal force.

How to Calculate centrifugal force?

To calculate the centrifugal force experienced by an object, such as the stone in the example given, you can follow these steps:

1. Determine the mass (m) of the object. In the example, the mass of the stone is given as 5 kg.
2. Determine the length or distance (r) from the center of rotation to the object. In the example, the length of the string is given as 10 m.
3. Determine the velocity of the object. This can be either the tangential velocity (v) or the angular velocity (ω). If the angular velocity is known, the tangential velocity can be calculated using the formula v = ω × r. In the example, let’s assume the tangential velocity is given as 5 m/s.
4. Use the following formula to calculate the centrifugal force:

Centrifugal force = m × v² / r

Plugging in the values from the example:

Centrifugal force = 5 kg × (5 m/s)² / 10 m

Simplifying the calculation:

Centrifugal force = 5 kg × 25 m²/s² / 10 m

Centrifugal force = 125 kg·m/s² / 10 m

Centrifugal force = 12.5 N

Therefore, the calculated centrifugal force for the given example is 12.5 Newtons (N).

Applications of Centrifugal force

Despite being a hypothetical force in Newton’s theories, centrifugal force has multiple practical uses in a variety of industries. Among the famous applications of centrifugal force are:

• Centrifuges: Centrifuges work on the centrifugal force principle. Centrifuges generate a centrifugal force that separates particles based on their densities by spinning samples at high speeds. Denser particles migrate outward, while less dense particles move inward, enabling for efficient substance separation and analysis.
• Centrifugal Governors: Centrifugal governors are used in engines to keep the speed steady. These devices use centrifugal force to control the flow of fuel or working fluids, allowing the engine’s speed to be adjusted by modifying the throttle or valve position. The system’s response is determined by the centrifugal force exerted on the governor’s rotating components.
• Artificial Gravity in Space Stations: Centrifugal force is used to imitate the effects of gravity in rotating space stations. By rotating the station, the centrifugal force acts outward from the centre, giving the inhabitants the impression of gravity. This approach enables for longer stays in space by mitigating the negative effects of extended weightlessness on the human body.
• Washing Machine Dryers: Centrifugal force is used by washing machine dryers to remove surplus water from freshly washed garments. When the drum rotates quickly, centrifugal force forces the clothing outward, pressing them against the chamber walls. As a result, water is driven out of the drum through the holes, speeding up the drying process.
• Amusement Park Rides: To deliver thrilling sensations, several amusement park rides use centrifugal force. Gravitron and Round-Up rides use spinning platforms that rotate quickly, generating centrifugal force. This force pushes passengers into the ride’s walls, giving them the sensation of being lifted off the floor and pressed against the wall.

These applications demonstrate centrifugal force’s practical utility in a variety of domains, ranging from scientific research and industrial procedures to everyday comforts and leisure pursuits. Despite the fact that centrifugal force is a fictitious force in Newtonian mechanics, understanding and harnessing it allows for the development of creative technology and improves our understanding of physical events.

Examples of Centrifugal force

In our daily lives, centrifugal force presents itself in a variety of ways. Here are some examples of the presence of centrifugal force:

• Car Turns: When a car turns, the passengers feel an outward force. This force pushing them into the car’s side is an example of centrifugal force. It’s caused by their inertia trying to keep them travelling in a straight path while the car reverses direction.
• Spin Dryer: In a spin dryer or centrifugal dryer used in laundry, clothes are rapidly spun inside a drum. As the drum rotates, the centrifugal force expels water from the clothes, allowing them to dry faster than through air drying alone.
• Bicycle Turns: When riding a bicycle and making a turn, the rider leans inward to counteract the centrifugal force and maintain balance. This adjustment helps keep the bicycle and rider stable while navigating the curved path.
• Roller Coasters: Roller coasters often incorporate sharp turns and loops. As the cars traverse these curves, passengers feel an outward force pushing them against the sides of the cars. This sensation is a result of the centrifugal force acting due to the rapid change in direction.
• Whirling Stone: The force exerted on the hands holding the string when a stone is whirled around in a circular motion by a string is due to centrifugal force. The inertia of the stone resists changes in its straight-line motion, resulting in a tension force in the string that counteracts the draw towards the centre.
• Carnival Rides: Various amusement park rides utilize centrifugal force to provide thrilling experiences. For example, the Gravitron ride features a spinning platform that rotates rapidly. Passengers inside the ride are pushed against the walls by centrifugal force, creating the sensation of defying gravity.
• Planetary Orbits: In our solar system, the centrifugal force is involved in the orbits of planets around the Sun. The gravitational pull of the Sun provides the centripetal force that keeps the planets in their orbits, while the centrifugal force acts as a balancing force, preventing the planets from falling into the Sun.
• The Earth’s form: Another illustration of the influence of centrifugal force is the form of the Earth. Because of the planet’s rotation, the Earth is flattened at the poles and bulged at the equator. The equatorial region bulges outward as a result of the centrifugal force created by the Earth’s rotation.
• Water in a Rotating Bucket: When a bucket filled with water is rotated in a circular direction, the water within does not fall out due to force balancing. The centrifugal force pressing on the bucket counteracts the weight of the bucket, preventing the water from flowing out.
• Water Park Slides: Water slides often have curves and loops where riders experience centrifugal force. As riders descend through these turns, the curved shape of the slide and the rider’s inertia generate an outward force that enhances the excitement of the slide.
• Mud on Car Wheels: When a vehicle travels through mud, mud particles tend to adhere to the wheels. The centrifugal force acts on the mud particles as the wheels move, causing them to be thrown tangentially towards the mudguard. This phenomenon explains why mud is frequently observed splattered on the sides of automobile wheels.
• Revolving Doors: Revolving doors in buildings employ centrifugal force to allow smooth and controlled entry and exit. As people push against the door and walk forward, the rotating motion of the door utilizes the centrifugal force to move people around the curve and maintain a constant speed.

These examples demonstrate the presence and effects of centrifugal force in everyday situations, exhibiting how it affects motion, forms, and diverse phenomena. Understanding centrifugal force enables us to analyse and anticipate the behaviour of systems that involve circular motion and rotation.

Centrifugal force vs Centripetal force

Centripetal force and centrifugal force are two interconnected notions that are critical in comprehending circular motion. Let us contrast the two forces:

• Definition: Centripetal force is defined as the force acting on a body travelling in a circular path along the radius, directed towards the centre of the circle. Centrifugal force, on the other hand, is an outward imaginary force experienced by an item travelling on a circular path away from the centre of rotation.
• Nature: Centripetal force is a real force with real effects on objects moving in circles. It is directly responsible for maintaining an object’s circular route. Centrifugal force, on the other hand, is regarded as a false or pseudo force. It has genuine consequences and is observed from a rotating frame of reference, while not being a fundamental force.
• Direction: Centripetal force is always directed towards the centre of the rotating circle. It is the inward force that keeps an item from travelling in a straight line tangent to a circle. Centrifugal force, on the other hand, is directed away from the centre of the circle of revolution. It works as an outer force, drawing items away from the centre.
• Role: Centripetal force is required for circular motion. An object cannot maintain a curved route without it and will move in a straight line. Centripetal force is what causes an object’s velocity to change direction, keeping it in a circular orbit. In contrast, centrifugal force does not exist independently. It is caused by the interaction of two objects and is connected to the object’s inertia in circular motion.
• Origin: Centripetal force is caused by the interaction of an item in circular motion with the source of the force, such as gravitational attraction or string tension. Centrifugal force, on the other hand, is caused by the object’s inertia. It is caused by the object’s proclivity to resist changes in straight-line motion.
• Formula: Centripetal force can be estimated using a variety of formulas, depending on the situation and the type of force involved, such as gravitational force or tension force. The centrifugal force formula is sometimes represented as the inverse of the centripetal force formula, indicating that the two forces have identical magnitude but opposing directions.
• Action: Centripetal force has an effect in both inertial and non-inertial frames of reference. It exists and is required to maintain circular motion independent of frame of reference. Centrifugal force, on the other hand, can only be observed in a rotating frame of reference or in non-inertial frames. It appears to counteract centripetal force and account for the apparent outward force felt by objects moving in a circular motion.

Aspects	Centripetal force	Centrifugal force
Definition	The force acting on a body moving in a circular path along the radius, directed towards the center of the circle.	An outward fictitious force experienced by an object moving in a circular path, directed away from the center of rotation.
Nature	Real force with real effects.	Considered a fictitious or pseudo force but has real effects.
Direction	Directed towards the center of the circle of rotation.	Directed away from the center of the circle of rotation.
Role	Essential for circular motion.	Does not have an independent existence.
Origin	Arises from the interaction between the object and the source of the force.	Originates from the inertia of the object.
Formula	Dependent on the specific scenario and type of force involved.	Often expressed as the negative of the centripetal force formula.
Action	Acts in both inertial and non-inertial frames of reference.	Acts only in the rotating frame (non-inertial frames).

FAQ

References

• Khatry MK et al. Principles of Physics. Aayam Publications.
• https://thefactfactor.com/facts/pure_science/physics/centripetal-force/6311/
• https://en.wikipedia.org/wiki/Centrifugal_force_(rotating_reference_frame)
• https://www.sarthaks.com/204136/stone-tied-string-length-whirled-vertical-circle-with-the-other-end-the-string-the-centre
• https://www.livescience.com/52488-centrifugal-centripetal-forces.html
• https://www.sciencedirect.com/topics/earth-and-planetary-sciences/centrifugal-force
• https://www.britannica.com/science/centrifugal-force
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• https://driversed.com/driving-information/driving-conditions/understanding-centrifugal-and-centripetal-forces/
• https://www.diffen.com/difference/Centrifugal_Force_vs_Centripetal_Force