# Centrifugal force- Definition, Principle, Examples (vs Centripetal force)

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Have you ever felt a push or a pull when you are in a moving vehicle that takes a sharp turn or a curve? Have you ever wondered why the water in a bucket doesn`t spill when you swing it in a circular motion? Have you ever noticed how the clothes in a washing machine get dry after spinning? These are some of the examples of **centrifugal force**, which is one of the most fascinating and widely used concepts in physics.

Centrifugal force is an **outward** force that is experienced by an object moving in a **circular** path. It is directed **away** from the center of rotation and is **parallel** to the axis of rotation. It is also called a **fictitious** or **pseudo** force because it does not exist in an inertial frame of reference. It only appears when there is another force, called the **centripetal** force, that acts **towards** the center of rotation and keeps the object in circular motion. The centrifugal force is equal in **magnitude** and **dimensions** to the centripetal force, but opposite in **direction**. The centrifugal force depends on the **mass**, the **distance** from the center, and the **speed** or **angular velocity** of the object. The unit of centrifugal force is **Newton (N)** and the dimensional formula is M^{1}L^{1}T^{-2}. The concept of centrifugal force has been used in various rotating devices like centrifuges, banked roads, and centrifugal pumps.

The centrifugal force is the outward force that acts on an object moving in a circular path. It depends on three factors: the mass of the object, the distance of the object from the center of rotation, and the speed of rotation. There are two ways to calculate the centrifugal force, depending on whether you know the tangential velocity or the angular velocity of the object.

### Tangential velocity

The tangential velocity is the speed of the object along the circular path. It is measured in meters per second (m/s) or kilometers per hour (km/h). If you know the tangential velocity of the object, you can use this formula to calculate the centrifugal force:

F_{c} = m * v^{2} / r

where

- F
_{c}is the centrifugal force in newtons (N) - m is the mass of the object in kilograms (kg)
- v is the tangential velocity in meters per second (m/s)
- r is the radius of the circular path in meters (m)

For example, if a car with a mass of 1000 kg is moving at a speed of 20 m/s along a circular road with a radius of 50 m, the centrifugal force acting on the car is:

F_{c} = 1000 * 20^{2} / 50

F_{c} = 8000 N

### Angular velocity

The angular velocity is the rate of change of the angle of the object along the circular path. It is measured in radians per second (rad/s) or revolutions per minute (rpm). One radian is equal to 57.3 degrees, and one revolution is equal to 2π radians. If you know the angular velocity of the object, you can use this formula to calculate the centrifugal force:

F_{c} = m * ω^{2} * r

where

- F
_{c}is the centrifugal force in newtons (N) - m is the mass of the object in kilograms (kg)
- ω is the angular velocity in radians per second (rad/s)
- r is the radius of the circular path in meters (m)

To use this formula, you need to convert the angular velocity from rpm to rad/s by multiplying it by 2π/60. For example, if a bicycle wheel with a mass of 2 kg and a radius of 0.3 m is spinning at 120 rpm, the centrifugal force acting on a point on the rim of the wheel is:

ω = 120 * 2π / 60

ω = 12.57 rad/s

F_{c} = 2 * 12.57^{2} * 0.3

F_{c} = 59.5 N

As discussed above, the centrifugal force is fictitious or pseudo as it only exists when a centripetal force is present. To understand the principle of centrifugal force, let us consider some examples.

### Example 1: Car with passengers

When a car with passengers turns the wheel, the vehicle is driven by the centripetal force that acts on all parts of the vehicle. However, the passengers in the car retain the freedom of their movement and thus maintain a straight path when the vehicle begins to turn. This causes the passengers to move towards the edge of the seat towards the door, which transmits the centripetal force to the passengers. The force experienced by the passengers away from the car is the centrifugal force.

In this diagram, F_{c} is the centripetal force acting on the car, F_{p} is the centripetal force acting on the passenger, and F_{cf} is the centrifugal force experienced by the passenger.

### Example 2: Stone at the end of a string

When a stone at the end of a string tied to a pole on the ground is rotated, the direction of the velocity of the stone changes continuously, which creates acceleration. If the string breaks, the stone tends to retain its inertia and move in a straight line tangent to the circular path. If the centrifugal force was real, the stone would move in an outwards direction instead of moving tangentially.

In this diagram, F_{c} is the centripetal force acting on the stone, F_{t} is the tension in the string, and F_{cf} is the centrifugal force experienced by the stone.

Newton’s law of motion doesn’t consider this a real force as according to Newton’s second law of motion, acceleration is caused by force. The centrifugal force is not caused by any physical interaction but by inertia. Therefore, it is called a fictitious or pseudo force.

The principle of centrifugal force can be explained by using different frames of reference. A frame of reference is a system that defines how an observer measures position, velocity, and acceleration. There are two types of frames of reference: inertial and non-inertial.

An inertial frame of reference is one that moves with constant velocity or remains at rest. In an inertial frame of reference, Newton’s laws of motion are valid and no fictitious forces are needed to explain motion.

A non-inertial frame of reference is one that accelerates or rotates relative to an inertial frame of reference. In a non-inertial frame of reference, Newton’s laws of motion are not valid and fictitious forces are needed to explain motion.

In our examples, an observer on the ground is in an inertial frame of reference and can explain the motion of the car or the stone by using only centripetal force. However, an observer in the car or attached to the stone is in a non-inertial frame of reference and needs to introduce centrifugal force to explain their motion.

The centrifugal force can be considered as a correction term that allows us to use Newton’s laws of motion in a rotating or accelerating frame of reference. It is important to note that centrifugal force does not cause any change in motion but only balances out other forces in a non-inertial frame of reference.

I hope this helps you understand the principle of centrifugal force better. 😊

To calculate the centrifugal force experienced by an object moving in a circular path, we need to know three things: the mass of the object (m), the distance of the object from the center of rotation (r), and the velocity of the object (v). The velocity can be either tangential velocity or angular velocity. Tangential velocity is the speed of the object along the tangent to the circular path, and angular velocity is the rate of change of angle of the object with respect to the center of rotation.

The formula for calculating the centrifugal force depends on which type of velocity we are given. If we are given the tangential velocity, we can use this formula:

F_{c} = m * v^{2} / r

where F_{c} is the centrifugal force, m is the mass, v is the tangential velocity, and r is the distance from the center.

If we are given the angular velocity, we can use this formula:

F_{c} = m * ω^{2} * r

where ω is the angular velocity, and the other symbols are as before.

The unit of centrifugal force is Newton (N), and its dimensional formula is M^{1}L^{1}T^{-2}.

Let us see an example of how to calculate the centrifugal force using both formulas.

**Example:** A ball of mass 0.5 kg is attached to a string of length 1 m and is whirled in a horizontal circle with a tangential velocity of 4 m/s. What is the centrifugal force acting on the ball?

**Solution:** Using the first formula, we get:

F_{c} = m * v^{2} / r

F_{c} = 0.5 * 4^{2} / 1

F_{c} = 8 N

Using the second formula, we need to find the angular velocity first. The angular velocity can be calculated as:

ω = v / r

ω = 4 / 1

ω = 4 rad/s

Then, we get:

F_{c} = m * ω^{2} * r

F_{c} = 0.5 * (4)^{2} * 1

F_{c} = 8 N

We get the same answer using both formulas, as expected.

Even though Newton’s law doesn’t consider the centrifugal force a real one, it has multiple applications:

**Centrifuges**operate on the principle of centrifugal force. The centrifugal force created due to the rotors induces a hydrostatic pressure gradient in the tubes directed perpendicular to the axis of rotation. This results in larger buoyant forces that push the less dense particles inwards while the denser particles are moved outwards. This principle allows the separation of particles on the basis of their densities.- The
**centrifugal governor**is a system that maintains a constant speed in an engine by moving the fuel or working liquid radially which is caused by the centrifugal force. - Centrifugal forces are used to generate
**artificial gravity**in rotating space stations. These stations help to study the effects of gravity of other planets in a simulated way. - Centrifugal force is also used by
**washing machine dryers**where the spinning of the rotor in a washing machine generates a centrifugal force that causes the clothes to move away from the center. This causes the water to be forced out of the wet clothes through the holes present in the chamber. - Centrifugal forces are used in various
**rides in amusement parks**where the force pushes the riders against the wall and allows the passengers to be raised above the floor of the machines.

Centrifugal force can be seen in various processes in our daily life; some examples are given below:

- The force acting on the passengers outwards in a car when the car is taking a turn is an example of centrifugal force. This is because the passengers tend to maintain their inertia and move in a straight line, while the car changes its direction. The passengers feel a push towards the door of the car, which is the centrifugal force.
- When a stone tied to a string is whirled in a circle, the force exerted on the hands is also because of centrifugal force. This is because the stone tries to move away from the center of rotation due to its inertia, but the string prevents it from doing so. The string exerts a tension force on the stone, which is equal and opposite to the centrifugal force acting on the stone.
- The earth is flattened at the poles and bulged at the equator because the centrifugal force acting on the particles at the equator is maximum. This is because the earth rotates about its axis, and the particles at the equator have a higher tangential velocity than those at the poles. The centrifugal force causes the particles at the equator to move away from the center of gravity of the earth, creating a bulge. The particles at the poles are closer to the center of gravity and experience less centrifugal force, creating a flattening effect.
- When a bucket filled with water is rotated in a circle, the water in the bucket doesn’t fall because the weight of the bucket is balanced by the centrifugal force acting on the bucket. This is because when the bucket is rotated, the water inside it also rotates with it and tries to move away from the center of rotation due to its inertia. The bucket exerts a normal force on the water, which is equal and opposite to the centrifugal force acting on the water. The resultant force on the water is zero, and it stays inside the bucket.
- The mud stuck on the wheels of cars is thrown tangentially towards the mudguard as a result of centrifugal force. This is because when the wheels rotate, the mud on them also rotates with them and tries to move away from the center of rotation due to its inertia. The mudguard exerts a frictional force on the mud, which is opposite to its tangential velocity. The resultant force on the mud is not zero, and it flies off tangentially from the wheel.

Centrifugal and centripetal forces are both related to circular motion, but they have some differences. Here are some of the main points of comparison between them:

**Direction:**Centrifugal force is an outward force that acts away from the center of rotation, while centripetal force is an inward force that acts towards the center of rotation.**Nature:**Centrifugal force is a fictitious or pseudo force that arises due to the inertia of the moving body, while centripetal force is a real force that causes the circular motion of the body.**Frame of reference:**Centrifugal force is observed in a rotating frame of reference, while centripetal force is observed in an inertial frame of reference.**Formula:**Centrifugal force and centripetal force have the same magnitude and dimensions, but opposite directions. The formula for both forces is given by: F = mω^{2}r = mv^{2}/r where m is the mass of the body, ω is the angular velocity, v is the tangential velocity, and r is the radius of the circular path.**Examples:**Some examples of centrifugal force are: the outward push on passengers in a car when it takes a turn, the separation of particles in a centrifuge, and the bulging of the earth at the equator. Some examples of centripetal force are: the tension in the string that holds a whirling stone, the gravitational force that keeps the moon in orbit around the earth, and the frictional force that prevents a car from skidding on a curved road.

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