Section 12–5 Pseudo forces

(Centrifugal force / Horizontal pseudo force / Gravity)

In this section, Feynman discusses centrifugal force, horizontal pseudo force, and gravity. A pseudo force is sometimes known as a fictitious force, inertial force, or d’Alembert force.

1. Centrifugal force:

“Another example of pseudo force is what is often called ‘centrifugal force’ (Feynman et al., 1963, section 12–5 Pseudo forces).”

Feynman gives an example of a pseudo force that is also known as “centrifugal force.” He adds that an observer in a rotating coordinate system, e.g., in a rotating box, will look for unknown forces that throwing things toward the walls (outwardly). According to Feynman, the centrifugal force is simply due to the fact that the observer does not have Newton’s coordinate system or the simplest coordinate system. In a sense, centrifugal force is a corrective term invented in a non-inertial frame of reference such that Newton’s second law of dynamics still holds. To be precise, one may explain that the centripetal force is a real force that is measurable by an observer in an inertial frame of reference, whereas the centrifugal force is a “corrective force” that is deducible by an observer in a rotating frame of reference.

In Principia, Newton describes an experiment of a rotating bucket of water and explains the parabolic shape of the water surface. He idealizes the water rotates with respect to absolute space. In 1966, Feynman declined a suggestion of the editor of The Physics Teacher to discuss a sprinkler problem that is related to a centrifugal force and objected to it being called “Feynman’s problem” (Feynman, 2005, p. 211). His reason was this problem is discussed in Mach’s (1883) “The Science of Mechanics.” Mach argues that the parabolic shape of the water surface in a rotating bucket should be explained in relation to the rest of the matter in the universe. Notably, Feynman discussed Mach’s principle with Wheeler before performing a sprinkler’s experiment that led Feynman banished from the lab (Wheeler, 1989).

2. Horizontal pseudo force:

“…because of the horizontal acceleration there is also a pseudo force acting horizontally and in a direction opposite to the acceleration (Feynman et al., 1963, section 12–5 Pseudo forces).”

Another example of a pseudo force can be illustrated by pushing a jar of water (e.g., to the right) along a table such that there is an acceleration. Feynman explains that the pseudo force is acting horizontally (to the left) and in a direction opposite to the acceleration. The resultant of the pseudo force and gravitational force makes an angle with the vertical, and the surface of the water is perpendicular to the resultant force during the acceleration (the water in the “backward” side of the jar moves upward.) When the jar decelerates because of a frictional force (e.g., to the left), the pseudo force is reversed (to the right) and the water in the “forward” side of the jar moves upward (Fig. 12–4). In short, the water surface is perpendicular to the effective gravity (as a result of the pseudo force).

The angle of inclination of the water surface is dependent on the horizontal push or frictional force; the angles need not be the same in both cases. We can have an alternative explanation on the angle of inclination of the water surface. In the case of acceleration (horizontal push), a water molecule on the water surface appears stationary because the pseudo force that is acting toward the left is balanced by the horizontal component of a normal reaction (to the right) on the water molecule. In the case of retardation (frictional force), a water molecule on the water surface appears stationary because the pseudo force that is acting toward the right is balanced by the horizontal component of a normal reaction (to the left) on the water molecule. The water molecule’s weight is balanced by the vertical component of the normal reaction.

3. Gravity:

“The possibility exists, therefore, that gravity itself is a pseudo force (Feynman et al., 1963, section 12–5 Pseudo forces).”

Feynman asks whether gravity is a pseudo force simply because we do not have the right coordinate system. For instance, a man in a stationary box on the earth finds himself held to the floor of the box with a gravitational force. Assuming there was no earth at all and an enclosed box moves with an acceleration g, then the man in the box might deduce a pseudo force (or gravity) which would pull him to the floor. In a sense, it is difficult to distinguish to what extent a given force is gravity and pseudo force, based on Einstein’s principle of equivalence. Some physicists may expect Feynman to clarify that the equivalence principle is, an approximation, within a small region of space. However, Feynman questions the principle by asking what happens to the people in Madagascar, on the other side of the earth—are they accelerating too?

There is no agreement among physicists whether gravity is a real force or pseudo force. Advocates that gravity is a real force may suggest one to drop an iPhone on his feet, and check whether it really hurts. On the other hand, some may argue that a pseudo force is real when one is in an accelerating car that experiences an injury or a real impact. However, in a graduate course on gravitation, Feynman clarifies that “[i]t is not possible to cancel out gravity effects entirely by uniform accelerations… It is true that we cannot imitate gravity with accelerations everywhere, that is, if we consider boxes of large dimensions (Feynman et al., 1995, pp. 91-92). In essence, it is possible to distinguish an acceleration from the gravitational force in a sufficiently large region (as compared to an infinitesimally small region).

Questions for discussion:

1. Is centrifugal force real or fictitious?

2. How would you explain the angle of inclination of the water surface in a jar while it is accelerating or decelerating on a table?

3. Is gravitational force real or fictitious?

The moral of the lesson: the centrifugal force is a pseudo force that is deducible by another observer in a rotating frame of reference, but it is difficult to define precisely to what extent an observed force is due to gravity or acceleration.

References:

1. Feynman, R. P. (2005). Perfectly reasonable deviations from the Beaten track: The letters of Richard P. Feynman (M. Feynman, ed.). New York: Basic Books.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

3. Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1995). Feynman Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley.

4. Mach, E. (1883/1989). The Science of Mechanics. La Salle, IL: Open Court.

5. Wheeler, J. A. (1989). The Young Feynman. Physics Today, 42(2), 24-28.