# Pseudo force | Fictitious force – Definition, Examples and Formula (Simple Explanation)

Imagine, you are driving a car.

Do you feel like someone is pushing you backwards when a car accelerates forward?

Imagine, you are in an elevator.

Do you feel like someone is pushing you downwards when an elevator accelerates upwards?

Imagine, you are enjoying a carousel (merry-go-round) ride.

Do you feel like getting thrown away when a carousel rotates in a circular path?

In all the above cases,

Do you know which magical force is acting on you?

This magical force is nothing but a pseudo force.

Only because of a pseudo force, you feel like…

Someone is pushing you backwards, while you are in a car.

Someone is pushing you downwards, while you are in an elevator.

You are getting thrown away, while you are on a carousel.

But the question is, what is pseudo force?

Don’t worry.

I’ll make you understand the exact meaning of pseudo force with practical examples. (Step by Step)

Let’s start off with the definition of pseudo force.

## Pseudo force definition

Do you know,

What is the meaning of the word “pseudo” in the definition of pseudo force?

It’s simple.

The word “pseudo” simply means Fake or Unreal.

Force is a push or pull on an object. (According to the definition of force)

In this way, you can easily remember the meaning of pseudo force.

Now,

The definition of pseudo force can be stated as:

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

(Pseudo force is also known as Fictitious force or Inertial force)

Let’s understand the above definition properly with practical examples.

So you’ll get an exact idea.

## Pseudo force examples

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

In simple language, the definition of pseudo force means that…

A pseudo force acts on an object only when an object’s frame of reference is accelerated.

In other words,

A pseudo force acts on an object only when an object is in the non inertial frame of reference.

(As you know, when a frame of reference is accelerated, it is known as non inertial frame of reference)

On the other hand,

A pseudo force will not act on an object when an object’s frame of reference is at rest or moving with constant velocity.

In other words,

A pseudo force will not act on an object when an object is in the inertial frame of reference.

(As you know, when a frame of reference is at rest or moving with constant velocity, it is known as inertial frame of reference)

Let’s understand this using examples, so you’ll get an exact idea.

### #1 When a car starts

Imagine, you are watching a sports car race on a television with your friend.

Suppose that a sports car is initially at rest and after some time the car race begins.

When the car race begins, you’ll notice that a sports car is accelerated forward by a car driver.

At this moment,

Do you know, there is one force acting on a car driver which pushes him backwards?

This force is nothing but a pseudo force

In other words,

A pseudo force is acting on a car driver which pushes him backwards.

See this,

As you can see,

A car driver experiences a pseudo force backwards, when he accelerates his car forward.

Now the question is,

Why don’t we notice this pseudo force acting on a car driver, while watching a car race from a tv?

What’s the reason behind this?

I think the reason is simple.

See this,

When a car driver accelerates his car, he is in the frame of reference which is accelerated.

On the other hand,

When we are watching a race on a tv, we are in the frame of reference which is not accelerated.

That’s the reason why we don’t notice a pseudo force and only a car driver experiences a pseudo force.

(As you know, pseudo force is always experienced in the non inertial frame of reference)

Therefore,

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

(i.e., an object’s frame of reference must be accelerated, then only an object will experience a pseudo force)

### #2 When a car stops

This is a similar example as seen above.

Imagine, you are watching a sports car race on a television with your friend.

But in this case,

Consider that a sports car is accelerating and the car race is about to end in some time.

When the car race ends, you’ll notice that a sports car is stopped by a car driver.

At this moment, there is a force acting on a car driver which pushes him forward.

In other words,

A pseudo force is acting on a car driver which pushes him forward.

See this,

As you can see,

A car driver experiences a pseudo force forward, when he stops his car.

The same question arises here,

Why don’t we notice this pseudo force acting on a car driver, while watching a car race on a tv?

The reason is simple.

Pseudo force is always experienced in the non inertial frame of reference.

In other words,

A car driver is in the frame of reference which is accelerated.

On the other hand,

We are in the frame of reference which is not accelerated.

That’s the reason why we don’t notice a pseudo force and only a car driver experiences a pseudo force.

See this,

Here’s the interesting part,

You might be thinking that…

How the frame of reference of a car driver is accelerated as he has stopped the car, right?

The reason is simple.

As you know, a car will not stop all of a sudden when the brakes are applied to it.

It means that,

The frame of reference of a car driver is still accelerated even after applying the brakes.

That’s why, a car driver experiences a pseudo force when he stops the car.

Therefore,

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

(That’s how you can remember the definition of pseudo force)

### #3 When a car is turned left

Imagine, you are in the audience and watching a sports car race along with your friend.

You’ll notice that different sports cars are running on a road with extremely high speed.

Suppose that a left turn comes on a road and a car driver turns his car towards the right.

At this moment,

Do you know, there is one fictitious force acting on a car driver which pushes him towards the right?

This fictitious force is a pseudo force.

In other words,

A pseudo force is acting on a car driver which pushes him towards the right.

See this,

As you can see,

A car driver experiences a pseudo force (fictitious force) towards the right, when he turns his car towards the left.

Now, you might be thinking that…

Why don’t we notice this fictitious force acting on a car driver, while watching a car race from an audience?

What should be the reason, according to you?

The reason is simple.

See this,

As you can see,

When a car driver turns his car towards the left, he is in the frame of reference which is accelerated.

On the other hand,

When we are sitting in an audience, we are in the frame of reference which is not accelerated.

That’s the reason why we don’t notice a pseudo force and only a car driver experiences it.

(As you know, pseudo force is always experienced in the non inertial frame of reference)

Therefore,

An object’s frame of reference must be accelerated, then only an object will experience a pseudo force.

In short,

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

### #4 When a car is turned right

This example is similar to the above one.

Imagine, you are in the audience and watching a sports car race along with your friend.

You’ll notice that different sports cars are running on a road with extremely high speed.

But in this case,

Suppose that a right turn comes on a road and a car driver turns his car towards the left.

At this moment,

One fictitious force acting on a car driver which pushes him towards the left.

This fictitious force is a pseudo force.

In other words,

A pseudo force is acting on a car driver which pushes him towards the left.

See this,

As you can see,

A car driver experiences a pseudo force (fictitious force) towards the left, when he turns his car towards the right.

Again,

The same question arises here…

Why don’t we notice this fictitious force acting on a car driver, while watching a car race from an audience?

What is the reason behind this according to you?

It’s simple.

See this,

You can see that,

When a car driver turns his car towards the right, he is in the frame of reference which is accelerated.

And

While we are watching a car race from an audience, we are in the frame of reference which is not accelerated.

Therefore, we don’t notice a pseudo force acting on a car driver and only a car driver experiences this fictitious force.

(As you know, pseudo force is a fictitious force which is always experienced in the non inertial frame of reference)

So in this way,

You can easily remember the pseudo force definition.

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

(i.e., an object will experience a pseudo force only if its frame of reference is accelerated)

### #5 An elevator accelerating upwards

Imagine, you are in a shopping mall and watching a boy going in an elevator.

Suppose that an elevator is initially at rest and after some time it will start accelerating upwards.

When an elevator accelerates upwards, you’ll notice that a boy is also accelerating upwards along with an elevator.

At this moment,

Do you know, there is one fictitious force acting on a boy which pushes him downwards?

This fictitious force is nothing but a pseudo force

In other words,

A pseudo force is acting on a boy which pushes him downwards.

See this,

You can see that,

A boy is experiencing a pseudo force downwards, when an elevator is accelerating upwards.

But the question is,

Why don’t you notice this pseudo force acting on a boy, while watching a boy from outside an elevator?

Has this question come into your mind?

The reason is simple.

Look,

As you know,

A pseudo force is a fictitious force which is always experienced in the non inertial frame of reference.

Now,

When an elevator accelerates upwards, a boy is in the frame of reference which is accelerated.

And on the other hand,

When you watch a boy from outside an elevator, you are in the frame of reference which is not accelerated.

Because of this reason,

We don’t notice this pseudo force acting on a boy and only a boy experiences this pseudo force.

That’s why,

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

### #6 An elevator accelerating downwards

This is a similar example as seen above.

Imagine, you are in a shopping mall and watching a boy going in an elevator.

But in this case,

Consider that an elevator is accelerating downwards and after some time it will come into rest.

When an elevator accelerates downwards, you’ll notice that a boy is also accelerating downwards along with an elevator.

At this moment,

One fictitious force acting on a boy which pushes him upwards.

This fictitious force is a pseudo force

In other words,

A pseudo force is acting on a boy which pushes him upwards.

See this,

You can see how a boy experiences a pseudo force downwards, when an elevator accelerates upwards.

Again, the same question arises that…

Why don’t you notice this fictitious force acting on a boy, while watching a boy from outside an elevator?

Do you know the reason?

It’s simple.

See this,

You can see that,

When an elevator accelerates downwards, a boy is in the frame of reference which is accelerated.

Whereas,

At the time when you watch a boy from outside an elevator, you are in the frame of reference which is not accelerated.

That’s the reason why we don’t notice a pseudo force acting on a boy and only a boy experiences it.

(As you know, pseudo force is always experienced in the non inertial frame of reference)

In short,

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

Imagine, you are sitting on a carousel and your mom is watching you from the ground.

Suppose that a carousel is initially at rest and after some time a carousel rotates in a circular path.

When a carousel rotates in a circular path, your mom notices you accelerating forward along with a carousel.

At this moment,

Do you feel one fictitious force acting on you which is throwing you outwards?

This force is nothing but a pseudo force

In other words,

A pseudo force is acting on you which is throwing you outwards.

See this,

As you can see,

A pseudo force is experienced outwards, when a carousel rotates in a circular path.

Now the question is,

Why don’t your mom notice this pseudo force acting on you, while watching from the ground?

What do you think of this question?

The reason is simple.

According to the pseudo force definition,

A pseudo force is always experienced in the non inertial frame of reference.

Therefore,

When you are sitting on a carousel and rotating in a circular path, you are in the frame of reference which is accelerated.

On the other hand,

When your mom is watching you from the ground, your mom is in the frame of reference which is not accelerated.

So, only you experience this pseudo force and your mom does not notice this pseudo force acting on you.

That’s why,

“A force that appears to act on an object whose motion is described using a non inertial frame of reference is known as pseudo force

## Pseudo force formula

From the above examples, it is clear that…

Object’s frame of reference must be accelerated, then only an object will experience a pseudo force.

And

In the above examples, have you noticed one thing?

A pseudo force always acts in the opposite direction to the acceleration of an object’s frame of reference.

In other words,

In whichever direction an object’s frame of reference is accelerated, a pseudo force will always act opposite to it.

Now, as you know…

According to Newton’s second law of motion,

Net force acting on an object depends upon both the mass as well as the acceleration. (i.e., Fnet = ma)

In a similar way,

The formula of pseudo force can be given as follows:

• Pseudo force formula: Fp = – ma

Where,

Fp = pseudo force acting on an object

m = mass of an object

a = acceleration of an object’s frame of reference

(-) sign indicates that pseudo force is acting in the opposite direction to the acceleration of an object’s frame of reference.

## Is pseudo force a real force?

According to the definition of pseudo force,

Pseudo force is experienced on an object when an object’s frame of reference is accelerated.

And the definition of real force states that:

“A force that is acting on an object due to physical interaction between the objects is known as Real force

So what do you think, is pseudo force a real force?

Are they both similar or different forces?

Well, the answer is NO. Both the forces are different.

Let’s take one example.

Imagine, you are sitting inside a car.

Suppose that a car driver accelerates a car forward.

At this moment,

Just for a second, do you feel like someone is pushing you backwards?

Obviously, Yes.

This backward push is nothing but a pseudo force.

Now,

You might be thinking that this pseudo force is a real force, right?

(As there is a physical interaction between you and the seat of a car)

If you are thinking so, you are wrong.

Let me show you how.

Imagine, you are standing on the ground (outside the car) and the same thing happens.

Again, a car driver accelerates a car forward.

What do you notice from the ground?

In this case,

You’ll notice that only a car is accelerating forward, right?

(Because while you are standing on the ground, you are in a inertial reference frame)

It means that while looking from the ground,

You’ll notice that a person sitting inside a car does not experience a pseudo force.

As you don’t notice a physical interaction occurring between a person and the seat of a car.

In short,

You’ll experience a pseudo force only when you are sitting inside a car.

(Because while you are sitting inside a car, you are in a non inertial reference frame)

That’s why,

“A pseudo force is a force that appears to act on an object whose motion is described using a non inertial frame of reference

Conclusion is,

Real force always acts on an object due to physical interaction between the objects.

(i.e., there must be an interaction between the objects for a real force to occur)

On the other hand,

Pseudo force is a fictitious force which acts on an object due to change in the object’s frame of reference.

(i.e., there is no interaction needed between the objects for a pseudo force to occur)

That’s why,

Pseudo force is not a real force. (It is a fictitious or a fake force)

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What do you think, is it easy for you to understand this concept of pseudo force?

(Let me know in the comments below)

### 2 thoughts on “Pseudo force | Fictitious force – Definition, Examples and Formula (Simple Explanation)”

1. well explained , thank you !