# Frequently Made Errors: Pseudo and Resultant Forces

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### 1. Real versus Fictitious

Pseudo, or “fictitious“, forces can arise when a non-inertial frame of reference is used. Using a non-inertial frame makes the usual force/acceleration laws fail. Pseudo forces must be added in to correct them.

### 2. Applied versus Resultant

The applied forces on an object are the specific forces exerted on it by other objects.  A resultant force is a force which would be equivalent to some combination of applied forces.

Pseudo forces act as though they are applied forces.

### 3. Inertia

For an accelerating mass m in an inertial frame we have the standard equations ##\vec {F_{net}} = \Sigma \vec F = m\vec a##.

If instead we use a reference frame with acceleration ##\vec {a’}##, the apparent acceleration will be ##\vec a – \vec {a’}##. To make the force equation right we have to add in a force ##\vec F_{a’} = -m\vec{a’}## to obtain

##\vec {F_{net}’} = \vec {F_{net}}+\vec F_{a’} = m\vec a-m\vec {a’}= m(\vec a – \vec {a’})##.

In the special case of a frame based on the mass itself, ##\vec a = \vec{a’}##, giving ##\vec {F_{net}’} =0##.

### 4. Centrifugal and Centripetal Forces

These are two ways of describing the force on an object associated with its movement in an arc.

• Centripetal view
X “In an inertial frame, the centripetal force is the applied force that makes the object move in an arc.”
Centripetal force is a resultant force, not an applied force.

“In an inertial frame, real applied forces have a real resultant force producing all the acceleration. The component normal to the velocity is termed the centripetal force.”

Degenerate example: A satellite in a circular orbit experiences the applied force of gravitational attraction to its host.  Since there are no other applied forces, this equals the resultant force.  Since the orbit is circular, this force is always perpendicular to the velocity, so it constitutes the centripetal force.

[Arguably, it is better to avoid the term centripetal force altogether and only refer to centripetal acceleration.]

• Centrifugal view
In the reference frame of the circling object, there is no radial acceleration. To get the forces to balance, we need to invent an applied force equal and opposite to the inertial frame’s centripetal force. This is termed the centrifugal force.
A centrifugal force* arises from tangential motion in a rotating reference frame.

Example: A motorcyclist on a “wall of death” experiences an increased reaction force from the saddle. This provides the centripetal force. To the motorcyclist, it feels like she is being pressed against the saddle by a centrifugal force.

### 5. Coriolis Force

A Coriolis force* arises from radial motion in a rotating reference frame.

Example: A skater spinning with arms outstretched draws his arms in to his chest.
Viewed in an inertial frame, conservation of angular momentum about the skater’s axis increases his angular speed.
To the skater, a Coriolis force exerts a torque acting on his arms.

*Some prefer to avoid the terms ‘centrifugal force’ and ‘Coriolis force’, referring instead to centrifugal and Coriolis accelerations.  It’s a matter of taste.  To an individual experiencing a rotation, it does feel like a force.  Since it is not an actual applied force, it is called a fictitious force.

12 replies
1. haruspex says:

1. Real versus Fictitious

Pseudo, or “fictitious“, forces can arise when a non-inertial frame of reference is used. Using a non-inertial frame makes the usual kinematic laws fail. Pseudo forces must be added in to correct them.

This statement is nonsense by definition of the term kinematics. Kinematics is, by definition, the description of motion without regard to forces. It uses whatever coordinate systems are convenient for the problem at hand, some likely to be inertial while other clearly are not, but all of that is irrelevant.

Yes, kinematics was the wrong word. I’ll correct it.

2. Let'sthink says:

I agree with the suggestion that the term term centripetal force be banned. One must understand that he term “centripetal” refers to a situation rather than an interaction. It is like calling some force as forward if it increases the speed and backward if it reduces the speed. Let us consider a point particle. what are the possibilities:
A. it is at rest permanently so a = 0 and resultant applied force on it is zero.
B. momentarily at rest, the one needs to find the direction and magnitude of its acceleration, a. “ma” will then be the the resultant externally applied force on the particle.
C. Moving in a straight line, find the direction and magnitude of its acceleration, a. “ma” will then be the the resultant externally applied force on the particle.
D. If the particle is moving along a curve, then, the resultant force on it may have a tangential component and a normal component. Normal component can change only the direction and not the speed and thecomponent tangential can only change the speed and not direction. This normal component is what we call centripetal force.

Coming to the term fictitious to centrifugal force is also not proper as its effects are real in a non inertial frame. The term pseudo is more preferable. It is teh term added to make Newton’s laws applicable to non-inertial frames.