Frequently Made Errors - Pseudo and Resultant Forces - Comments

[haruspex]

haruspex submitted a new PF Insights post

Frequently Made Errors - Pseudo and Resultant Forces

Continue reading the Original PF Insights Post.

 

[nasu]

The distinction between applied and resultant force may be confusing. And even misleading, when you say that the centripetal force cannot be "applied" but only resultant. What if there is only one force acting on the body in circular motion? What if there is a tangential force as well as a radial force? Will their resultant be the centripetal force?

 

[Overt]

A little confused about the applied vs resultant bit too. Having a hard time seeing the gravitational force on an orbitting planet as resultant but not "applied". Probably an issue with definitions I'm not getting.

Unless its saying that the centripetal is generally resultant. In the case of an orbitting planet, the gravitational force is the only force and it is an applied force which results in the centripetal force (consisting of only gravitation).

The distinction between applied and resultant force may be confusing. And even misleading, when you say that the centripetal force cannot be "applied" but only resultant. What if there is only one force acting on the body in circular motion? What if there is a tangential force as well as a radial force? Will their resultant be the centripetal force?

The key word in the definition given is that the centripetal force is a resultant force but not the resultant force. In general, systems don't have a single unique resultant force.

 

[vela]

Newton's second law says
$$\sum_{i=1}^n \vec{F}_i = \vec{F}_1+\vec{F}_2+\cdots+\vec{F}_n = m\vec{a}.$$ The $\vec{F}_i$'s are the forces acting on a body — that is, the applied forces. The centripetal force is not an applied force, so it doesn't appear as part of the sum of the forces. Note that in an inertial frame, an applied force should have a reaction counterpart, e.g., the Earth exerts a gravitational force on the Moon, and the reaction force is the Moon exerting a force on the Earth. In general, there is no reaction counterpart to the centripetal force because it's not an applied force.

I agree with the suggestion to avoid the term centripetal force altogether precisely because it leads to the misconception raised here. An object on a curved path instead experiences a centripetal acceleration $a_c = v^2/r$, where $v$ is the object's speed and $r$ is the radius of curvature.

 

[haruspex]

What if there is a tangential force as well as a radial force?

I was careful (I think) to refer always to the radial component of the resultant.

In the case of an orbitting planet, the gravitational force is the only force and it is an applied force which results in the centripetal force (consisting of only gravitation).

Exactly.

In general, systems don't have a single unique resultant force.

They don't? Well, they could reduce to a single force plus a screw ... but otherwise?

avoid the term centripetal force altogether

Interesting suggestion. I'll add that advice.

 

[haushofer]

I never understood all this buzz about "fictitious forces", or a statement like " Using a non-inertial frame makes the usual kinematic laws fail". No, it does not. The equation of motion just doesn't transform covariantly under (linear or rotational) accelerations, as it does under Galilei transformations. That's the whole deal. And because one can state Newton's laws, just as special or General relativity, in a coordinate-free way using differential geometry, there is no reason to single out inertial frames of reference.

When there are no forces, a particle follows a geodesic in Newtonian spacetime. This is a straight line, because space is flat. One can assign coordinate values to this line, giving that the second time derivative of x vanishes. If you then apply e.g. a time-dependent rotation R(t), such that x'=Rx, then automatically you get the centrifugal and Coriolis force. No talk about 'fictitious'.

 

[Ranku]

"Centrifugal view
In the reference frame of the circling object, there is no radial acceleration."
Of course there is radial acceleration: v^2/r.

 

[haruspex]

"Centrifugal view
In the reference frame of the circling object, there is no radial acceleration."
Of course there is radial acceleration: v^2/r.

In the reference frame of a given object, that object has no acceleration by definition.

 

[OldEngr63]

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 into 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.

 

[OldEngr63]

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

This is muddy thinking. There is a Coriolis acceleration that arises at times, but there is no Coriolis force. When the Coriolis acceleration is multiplied by a mass factor, the result is an inertial reaction term, an M*A term, but it is not a force.

(And no, Newton's Law does not say that any particular M*A term is a force. It says that the sum of all actual forces is equal to mass*acceleration of the cm for a particle (which is the particle location itself). Randomly chosen M*A terms are not forces, certainly not actual forces.)

 

[haruspex]

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

This is muddy thinking. There is a Coriolis acceleration that arises at times, but there is no Coriolis force. When the Coriolis acceleration is multiplied by a mass factor, the result is an inertial reaction term, an M*A term, but it is not a force.

(And no, Newton's Law does not say that any particular M*A term is a force. It says that the sum of all actual forces is equal to mass*acceleration of the cm for a particle (which is the particle location itself). Randomly chosen M*A terms are not forces, certainly not actual forces.)

The same objection can be made to the term "centrifugal force". Bear in mind that by definition a fictitious force is one that the observer invents to account for the experience, so it is reasonable to say that there is a Coriolis force. I'll try to make this clearer.

 

[haruspex]

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 into 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.

 

[Let'sthink]

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 the term added to make Newton's laws applicable to non-inertial frames.