Pseudo Force

Pseudo Force is a force that come into existence when the motion of an object is explained using non inertial frame of reference. The term pseudo means false, hence it is known by terms like fictitious forces or inertial forces. It can be understood as a force that seems to act on an object in a frame of reference that is not moving uniformly. These forces do not exist actually but are used to explain how an object moves in reference frames that are not fixed at a constant speed.

In this article, we will learn in detail about pseudo force, its definition, formula, examples and applications in real life domain.

What is Pseudo Force?

Pseudo force is a force that appears to be exerted on objects when they are viewed from a reference frame that is not accelerating. This force is also known as d’Alembert’s force. Pseudo Force are also called Fictitious Force because they are fictional in nature and not really exist. This force comes into action when the accelerating frame of reference(non-inertial frame of reference) starts accelerating, in comparison to the non-accelerating frame. The force does not arise from a physical interaction between the objects but from the fact that the non-inertial reference frame itself is accelerating.

The pseudo forces can be random, because they follow the acceleration of the frame. However, there are four commonly defined pseudo forces for frames that accelerate in specific ways: one for straight-line acceleration, two for rotation (Coriolis force and centrifugal force), and the one called the Euler force for variable rotation.

Pseudo Force Definition

Pseudo force is the apparent force that acts on the objects moving in a rotating or non-inertial frame of reference. Pseudo force happens when two frames of reference are accelerating relative to one another. Instead of actual contact between the objects, the force is due to the acceleration of the non-inertial reference frame.

Magnitude and Direction of Pseudo Force

Magnitude of Pseudo Force depends on both the acceleration and mass of an object. It is given by the following formula

F_p = ma

where,

• F_p is Pseudo Force
• m is mass of object
• a is acceleration

Direction of Pseudo Force is always opposite to the acceleration of the reference frame. It happens because of observing motion from a non-inertial frame wherein objects will seem to move or accelerate opposite to the real acceleration of the frame.

Pseudo Force Formula

Pseudo-forces are generally directed oppositely to that of an object’s acceleration in its reference frame. The formula for pseudo-force is as follows:

F_p = −ma

Where

• F_p = pseudo force that is acting on an object.
• m = object’s mass
• a = acceleration of object’s frame of reference

The negative sign here represents that this force is acting in the same direction as the acceleration of the item but against the frame of reference.

Explain Pseudo Force

Pseudo-forces are forces that look like they exist in frames of reference other than inertial ones. They are speeding up or rotating. Such forces are employed to illustrate the movements of objects in these frames. It should be mentioned that these forces are called pseudo or fictitious, since they are related to the acceleration of the reference frame, not to physical interactions between objects.

Phenomena of Pseudo Force in an Elevator

Consider the case of an elevator moving upwards with acceleration a. Of course, if a person is in the lift going upwards, they will sense an increase in their weight. This phenomenon can be attributed to a “pseudo-force” which is typically termed the “elevator force” or “pseudo-gravitational force”, that acts upon the person in the direction vertically downward.

Derivation of Pseudo Force

Let us derive the expression for the pseudo-force felt by the person in the elevator based on Newton’s law of motion.

If an elevator of total mass m has a person standing in there. The forces that are acting on the person here are:

Gravitational force (mg) acts downward (actual force).

Normal force (N) by the floor of the elevator upward (real force).

Acquired force (F_pseudo) acts upward due to the elevator’s acceleration.

Applying Newton’s Second Law

Net Force = Mass × Acceleration

N − mg + F_pseudo​ = m⋅a

By rearranging the equation, we get:

F_pseudo ​= m⋅(g+a)

where:

• F_pseudo is the pseudo force.
• m is the mass of the person.
• g stands for the acceleration due to gravity.
• a is the acceleration of the lift

The person will perceive a fictitious force pushing upward with magnitude m⋅(g+a) on the person and materialize as an increase in the weight.

It also shows us how pseudo forces help us understand the apparent consequences of acceleration in a non-inertial referential frame, such as an elevator.

Examples of Pseudo Force

Here are some examples of pseudo forces:

Lifting a box containing bricks

Imagine that a brick is enclosed within a box and that a piece of rope or a string is being pulled by the box. The box, building block, and the envelope surrounding them all float upwards, about the ground. The two look the same but in truth, the brick stays while the box moves. There is a counter-force exerted on the brick by an upward force while it is being pulled by gravity downward. Due to the frame’s acceleration, a pseudo force is generated here that is acting in the opposite direction.

The magnitude of the pseudo force is determined by multiplying the brick’s mass by the frame’s acceleration. Since the brick doesn’t move, the downward and upward force can be equal or zero(the brick’s net force = zero). Thus the pseudoforce and the gravitational force are of the same size, which is equal to the size of the net force.

Movement of Lift

A lift creates a strong upward force that lifts our body as we are getting up. This gives us an illusion that objects outside the elevator move at the same speed as the elevator but in the opposite direction and this is because of this force. The force that is responsible for causing things to move is known as pseudo force here.

Acceleration of Car

Each time the car runs at a higher speed we become used to feeling “pushed back into the seat”. From the perspective of someone in the car, there is no force pulling the driver backward. Instead, the car’s acceleration creates a fake force that pushes the driver’s frame of reference forward.

Applications of Pseudo Force

Here are some key applications of pseudo forces:

Rotating Reference Frames: These pseudo forces are extremely useful when trying to understand motion that takes place in rotating frames of reference, for example in a rotating planet, rotating machinery, or on a rotating vehicle such as a centrifuge.

Vehicle Dynamics: The pseudo forces play a great role when one is studying the motion of vehicles such as cars, airplanes, and ships. For example: when a car speeds up, passengers feel a backward fake force (inertia) due to acceleration.

Earth Sciences: In geophysics, pseudo forces are used to explain why objects move on the rotating Earth.

Mechanical Engineering: Pseudo forces play an important role in designing and analyzing machines with rotating or accelerating parts, such as engines, turbines, and gyroscopes.

Real-World Examples of Pseudo Force

Pseudo forces can be seen in everyday situations, which are as follows:

Car Acceleration: When a car accelerates, passengers experience the effect of the seat pushing back. This happens because the car is slow to change its speed and there is a force pulling it in the opposite direction of its acceleration.

Turning a Vehicle: When a car turns suddenly, passengers feel like being pushed toward the outside of the turn. We have here a force called the centrifugal force which occurs as a result of the inertia in the rotating frame of reference of the vehicle.

Spacecraft Maneuvers: In space, pseudo-forces have a significant role in guiding the movement of spacecraft. For instance, when you are accelerating or slowing down, astronauts onboard would feel a force due to inertia.

Pseudo Force vs Real Force

The difference between pseudo force and real force is tabulated below:

Feature	Pseudo Force	Real Force
Origin	Occurs in non-inertial reference frames	Occurs in inertial reference frames
Nature	Fictitious force is a term used to explain the way things seem to move.	Genuine force occurs when objects interact with each other.
Examples	Centrifugal force, Coriolis force	Friction, electromagnetic force, Gravitational force

Why Centrifugal Force is called a Pseudo Force

Centrifugal force is a force that appears to push items outwards from the center of rotation in a frame of reference that is rotating. But the object in a rotating frame tend to move in a straight line, following Newton’s first law of motion. However, because the frame is rotating, it appears as if a force is pushing objects outward. Hence, centrifugal force is a Pseudo Force.

Pseudo Force Frequently Asked Questions

What is the magnitude of pseudo force?

The magnitude of a pseudo force is directly proportional to the mass of the object being pushed by the force and the speed of the reference frame.

What is the direction of pseudo force?

The pseudo force is always directed opposite to the acceleration of the reference frame.

Why is pseudo-force negative?

The negative sign represents that this force is acting in the same direction as the acceleration of the item but against the frame of reference.

What is pseudo force formula?

Pseudo force formula is given as F_p = −ma where, m is mass of object and a is acceleration of non-inertial frame of reference

Is pseudo force real?

No, pseudo force is not real. It is fictious

What are four pseudo force?

The four pseudo force are rectilinear acceleration, coriolis force, centrifugal force and euler force