Misconceptions of Centripetal Force as the "Centrifugal Force" Michael Shaw, Applied Physics Student, Weber State University, 18 April 2012

Centripetal force is a place holder name for the force which essentially pulls an object towards the apparent center of its orbit or a circular path.3

FIG 1, Diagram of centripetal force for circular motion. copyright http://askphysics.com/centripetal-force-misconception/

This can be anything from the force of gravity between two orbiting bodies, a force of tension between a mass and a center-point connected by a string, force of wind resistance between air and a wing making a plane do a loop, the magnetic force between a magnetic field and a moving charged particle, or more often observed is the force of friction between the tires and the road while a car is turning around a corner. This is shown in Figure 1.

When a person thinks about the forces exerted upon them in their frame of reference in the case of a car turning around a corner, they commonly think of what has come to be known as a centrifugal force.4 Centrifugal force is an "imaginary" force which pulls in the opposite direction as the centripetal force. This is a pseudo-misconception based on the disregard or misunderstandings of the fundamentals of inertia, forces between two objects, and appropriate frames of reference. The reason this is a pseudo-misconception is because it has a place where it can be thought of semi-accurately, but it would be more accurate to take a proper reference frame to eliminate such confusion. Inertia | Forces Between Two Objects (always) | Inertial and Non-Inertial Reference Frames | The Non-Inertial Breakdown, the Inertial Correction | Concussion | References

Inertia

Newtons first law essentially states that an objects velocity will remain constant unless there is a non-zero net force acting upon it from another object. This is also called Newton's law of inertia. This means that any object which is not moving, or at constant velocity, has a net force acting upon it of zero. This does not mean there are no forces acting upon the object. The force of gravity pulls an object towards the center of the earths mass. If the object is remaining at rest, this means the normal-force from the earth is pushing against the object in the opposite direction of the force of gravity with equal magnitude. Therefore the net forces are zero. Now if an object is in motion, it will "want" to remain in the same straight-line motion. If this object was a body in a car, then it will want to continue in the straight-line direction when the car begins to turn. This tendency to continue straight-ward is the inertia. A fundamental concept to understand is F = ma, where F is a force, m is the mass of the object being acted upon, and a is the acceleration. Mass is a constant, meaning the accelerations are proportional to the force applied. Therefore, if the net forces = 0, there is a net acceleration of 0 as well.

Forces Between Two Objects (always)

Whenever one discusses forces, it is important that forces are always exerted between two objects for an inertial frame of reference. Concider pushing a

FIG 2, force diagram of a box on a surface, pulled by a string.

box. There will be the force of gravity pulling down on the box, and an equal and opposite normal force pushing up on the box. Now we have a pushing force in a horizontal direction, where the box exerts a pushing force in opposition, equal to the force of friction. If the box remains at rest, then the force of friction between the box and the surface must be equal and opposite to the force of pushing. If the box moves, the force of pushing must be greater than the force of friction in the opposite direction. This is still a set of forces acting in opposition, between two objects. The forces between the box and the earth, forces between the box and the surface, and the forces between the box and the thing doing the pushing. All of this is observed from a non-accelerating frame of reference, where we are looking at the system from the "outside" viewpoint. It is useful to review force diagrams for an example. Figure 2 shows the force diagram of a box, being pulled by a string. Again we see the force of gravity is equal to the normal force. At equilibrium, the force of static friction, Fs is equal to the force of tension, Ft. The force of tension is between the box and the object pulling it, and the force of friction is between the box and the surface. Therefore we see the forces are still acting between two objects.

Inertial and Non-Inertial Reference Frames

A inertial frame of reference is one where the perspective is not accelerating, or undergoing non-zero net forces. If you watch a car drive by on the road, and you are at a constant velocity (including a velocity of 0), you are an inertial frame of reference. This is the frame of reference which is classically taken when dealing with problems of forces and accelerations on objects in the system. The classical constructs of inertia, and forces between two objects begins to break down when you take a frame of reference which is undergoing accelerations. A non-inertial frame of reference would to take the frame of reference of a person riding on a merry-go-round.2 In this frame of reference, nothing on the merry-go-round is moving with respect to the merry-go-round. Another non-inertial frame of reference is the one perceived when turning a corner in a car. The driver and the car are heading in the same direction, and are accelerating in the same respective way; only the external system is moving with respect to the car and the driver.5

The Non-Inertial Breakdown, the Inertial Correction

When driving around a corner, the inertia of a body is tangential to the turn. From a non-inertial frame of reference, the car and the body are not moving, but a seemingly apparent force pulls the body away from the center. It can even make the body press hard against the side of the car door. The forces on the body would be a pushing force against the door, and an equal and opposite force if the body doesn't move with respect to the door. There is also the force of gravity equal and opposite to the normal force. This centrifugal force appears to not have an opposing force, it is a single force. This is a misconception of the behavior of forces, since we already know there should be a force acting between two objects, with an opposing force.4

If we step outside of the system and observe the car turning from above, we would see that the car and the body can be treated as a combined system. Now the forces acting on the car are the gravitational and normal forces, and the force of friction between the tires and the road. This force of friction is the centripetal force, which will accelerate the car towards the center of the circular path. The forces acting on the body are similar in behavior, we will have the force of gravity and the normal force, there will also be the force of friction between the body and the seat, and the pushing force between the body and the door. We now have all of the forces acting between two objects, where each exerts an opposing directional force.

Concussion

The term of centrifugal force is not referring to a force at all, but rather an object's inertia; energetically speaking, the momentum of the object. Proper forces should have opposing forces of varying magnitudes, where the net forces are equal to the net accelerations, acting between two or more objects. Taking a non-inertial reference frame will create a misconception of the forces being experienced. The feeling of a "centrifugal" force is really the feeling of being apart of a non-rigid system, where the momentum can transfer from the object in motion to the perceiving individual in motion. There may be other ways of getting the information across that Centrifugal force is not a force, but it seems the most foundation is made by teaching the concepts of inertia, forces, and reference frames correctly. This is a misconception that that many adults have, and a decreasing number of people as we get into younger ages. This is most likely do to the proportionality of the concept to the difficulty of the description. However, children would still be creating an idea of what is pulling them to the outside of the car, they just wouldn't have learned the word "Centrifugal" to describe the event. The actual event is still observed by the child, which is where we get the game "Leaners", where you lean in the direction the inertia is going to carry you, and crush your friend against the side of the car door.

http://xkcd.com/123/

References

Driver, R., Squires, A., Rushworth, P., & Wood-Robinson, V. (1994). Making Sense of Secondary Science. London and New York: Routledge.

Michael Shaw, Applied Physics Student, Weber State University, 18 April 2012

Centripetal forceis a place holder name for the force which essentially pulls an object towards the apparent center of its orbit or a circular path.3This can be anything from the force of gravity between two orbiting bodies, a force of tension between a mass and a center-point connected by a string, force of wind resistance between air and a wing making a plane do a loop, the magnetic force between a magnetic field and a moving charged particle, or more often observed is the force of friction between the tires and the road while a car is turning around a corner. This is shown in Figure 1.

When a person thinks about the forces exerted upon them in their frame of reference in the case of a car turning around a corner, they commonly think of what has come to be known as a

centrifugal force.4 Centrifugal force is an "imaginary" force which pulls in the opposite direction as the centripetal force. This is a pseudo-misconception based on the disregard or misunderstandings of the fundamentals of inertia, forces between two objects, and appropriate frames of reference. The reason this is a pseudo-misconception is because it has a place where it can be thought of semi-accurately, but it would be more accurate to take a proper reference frame to eliminate such confusion.Inertia | Forces Between Two Objects (always) | Inertial and Non-Inertial Reference Frames | The Non-Inertial Breakdown, the Inertial Correction | Concussion | References

InertiaNewtons first law essentially states that an objects velocity will remain constant unless there is a non-zero net force acting upon it from another object. This is also called Newton's law of inertia. This means that any object which is not moving, or at constant velocity, has a net force acting upon it of zero. This does not mean there are no forces acting upon the object. The force of gravity pulls an object towards the center of the earths mass. If the object is remaining at rest, this means the normal-force from the earth is pushing against the object in the opposite direction of the force of gravity with equal magnitude. Therefore the net forces are zero. Now if an object is in motion, it will "want" to remain in the same straight-line motion. If this object was a body in a car, then it will want to continue in the straight-line direction when the car begins to turn. This tendency to continue straight-ward is the inertia. A fundamental concept to understand is F = ma, where F is a force, m is the mass of the object being acted upon, and a is the acceleration. Mass is a constant, meaning the accelerations are proportional to the force applied. Therefore, if the net forces = 0, there is a net acceleration of 0 as well.

Forces Between Two Objects (always)Whenever one discusses forces, it is important that forces are always exerted between two objects for an inertial frame of reference. Concider pushing a

Inertial and Non-Inertial Reference FramesA inertial frame of reference is one where the perspective is not accelerating, or undergoing non-zero net forces. If you watch a car drive by on the road, and you are at a constant velocity (including a velocity of 0), you are an inertial frame of reference. This is the frame of reference which is classically taken when dealing with problems of forces and accelerations on objects in the system. The classical constructs of inertia, and forces between two objects begins to break down when you take a frame of reference which is undergoing accelerations. A non-inertial frame of reference would to take the frame of reference of a person riding on a merry-go-round.2 In this frame of reference, nothing on the merry-go-round is moving with respect to the merry-go-round. Another non-inertial frame of reference is the one perceived when turning a corner in a car. The driver and the car are heading in the same direction, and are accelerating in the same respective way; only the external system is moving with respect to the car and the driver.5

## The Non-Inertial Breakdown, the Inertial Correction

When driving around a corner, the inertia of a body is tangential to the turn. From a non-inertial frame of reference, the car and the body are not moving, but a seemingly apparent force pulls the body away from the center. It can even make the body press hard against the side of the car door. The forces on the body would be a pushing force against the door, and an equal and opposite force if the body doesn't move with respect to the door. There is also the force of gravity equal and opposite to the normal force. This centrifugal force appears to not have an opposing force, it is a single force. This is a misconception of the behavior of forces, since we already know there should be a force acting between two objects, with an opposing force.4

If we step outside of the system and observe the car turning from above, we would see that the car and the body can be treated as a combined system. Now the forces acting on the car are the gravitational and normal forces, and the force of friction between the tires and the road. This force of friction is the centripetal force, which will accelerate the car towards the center of the circular path. The forces acting on the body are similar in behavior, we will have the force of gravity and the normal force, there will also be the force of friction between the body and the seat, and the pushing force between the body and the door. We now have all of the forces acting between two objects, where each exerts an opposing directional force.

## Concussion

The term of centrifugal force is not referring to a force at all, but rather an object's inertia; energetically speaking, the momentum of the object. Proper forces should have opposing forces of varying magnitudes, where the net forces are equal to the net accelerations, acting between two or more objects. Taking a non-inertial reference frame will create a misconception of the forces being experienced. The feeling of a "centrifugal" force is really the feeling of being apart of a non-rigid system, where the momentum can transfer from the object in motion to the perceiving individual in motion. There may be other ways of getting the information across that Centrifugal force is not a force, but it seems the most foundation is made by teaching the concepts of inertia, forces, and reference frames correctly. This is a misconception that that many adults have, and a decreasing number of people as we get into younger ages. This is most likely do to the proportionality of the concept to the difficulty of the description. However, children would still be creating an idea of what is pulling them to the outside of the car, they just wouldn't have learned the word "Centrifugal" to describe the event. The actual event is still observed by the child, which is where we get the game "Leaners", where you lean in the direction the inertia is going to carry you, and crush your friend against the side of the car door.

## References

Making Sense of Secondary Science.London and New York: Routledge.American Journal of Physics, 53-71, http://modeling.asu.edu/R&E/Hestenes_CommonSenseConcept.pdf