Centrifugal force: According to the principle of Galilean relativity, if Newton’s laws are true in any reference frame, they are also true in any other frame moving at constant velocity with respect to the first one. Conversely, they do not appear to be true in any frame accelerated with respect to the first. Instead, in an accelerated frame, objects appear to have forces acting on them that are not in fact present. These are called pseudo forces, as described above. Since rotational motion is always accelerated motion, pseudo forces may always be observed in rotating frames of reference.
As one example, a frame of reference in which the Earth is at rest must rotate once per year about the Sun. In this reference frame, the gravitational force attracting the Earth toward the Sun appears to be balanced by an equal and opposite outward force that keeps the Earth in stationary equilibrium. This outward pseudo force, discussed above, is the centrifugal force.
The rotation of the Earth about its own axis also causes pseudo forces for observers at rest on the Earth’s surface. There is a centrifugal force, but it is much smaller than the force of gravity. Its effect is that, at the Equator, where it is largest, the gravitational acceleration g is about 0.5 percent smaller than at the poles, where there is no centrifugal force. This same centrifugal force is responsible for the fact that the Earth is slightly non spherical, bulging just a bit at the Equator.
Pseudo forces can have real consequences. The oceanic tides on Earth, for example, are a consequence of centrifugal forces in the Earth-Moon and Earth-Sun systems. The Moon appears to be orbiting the Earth, but in reality both the Moon and the Earth orbit their common centre of mass. The centre of mass of the Earth-Moon system is located inside the Earth nearly three-fourths of the distance from the centre to the surface, or roughly 4,700 kilometres from the centre of the Earth. The Earth rotates about this point approximately once a month. The gravitational attraction of the Moon and the centrifugal force of this rotation are exactly balanced at the centre of the Earth. At the surface of the Earth closest to the Moon, the Moon’s gravity is stronger than the centrifugal force. The ocean’s waters, which are free to move in response to this unbalanced force, tend to build up a small bulge at that point. On the surface of the Earth exactly opposite the Moon, the centrifugal force is stronger than the Moon’s gravity, and a small bulge of water tends to build up there as well. The water is correspondingly depleted at the points 90° on either side of these. Each day the Earth rotates beneath these bulges and troughs, which remain stationary with respect to the Earth-Moon system. The result is two high tides and two low tides every day every place on Earth. The Sun has a similar effect, but of only about half the size; it increases or decreases the size of the tides depending on its relative alignment with the Earth and Moon.
The Coriolis force is a pseudo force that operates in all rotating frames. One way to envision it is to imagine a rotating platform (such as a merry-go-round or a phonograph turntable) with a perfectly smooth surface and a smooth block sliding inertially across it. The block, having no (real) forces acting on it, moves in a straight line at constant speed in inertial space. However, the platform rotates under it, so that to an observer on the platform, the block appears to follow a curved trajectory, bending in the opposite direction to the motion of the platform. Since the motion is curved, and hence accelerated, there appears, to the observer, to be a force operating. That pseudo force is called the Coriolis force.
The Coriolis force also may be observed on the surface of the Earth. For example, many science museums have a pendulum, called a Foucault pendulum, suspended from a long cable with markers to show that its plane of motion rotates slowly. The rotation of the plane of motion is caused by the Coriolis force. The effect is most easily imagined by picturing the pendulum swinging directly above the North Pole. The plane of its motion remains stationary in inertial space, while the Earth rotates once a day beneath it.
At lower latitudes, the effect is a bit more subtle, but it is still present. Imagine that, somewhere in the Northern Hemisphere, a projectile is fired due south. As viewed from inertial space, the projectile initially has an eastward component of velocity as well as a southward component because the gun that fired it, which is stationary on the surface of the Earth, was moving eastward with the Earth’s rotation at the instant it was fired. However, since it was fired to the south, it lands at a slightly lower latitude, closer to the Equator. As one moves south, toward the Equator, the tangential speed of the Earth’s surface due to its rotation increases because the surface is farther from the axis of rotation. Thus, although the projectile has an eastward component of velocity (in inertial space), it lands at a place where the surface of the Earth has a larger eastward component of velocity. Thus, to the observer on Earth, the projectile seems to curve slightly to the west. That westward curve is attributed to the Coriolis force. If the projectile were fired to the north, it would seem to curve eastward.
The same analysis applied to a Foucault pendulum explains why its plane of motion tends to rotate in the clockwise direction anywhere in the Northern Hemisphere and in the counterclockwise direction in the Southern Hemisphere. Storms, known as cyclones, tend to rotate in the opposite direction in each hemisphere, also due to the Coriolis force. Air moves in all directions toward a low-pressure centre. In the Northern Hemisphere, air moving up from the south is deflected eastward, while air moving down from the north is deflected westward. This effect tends to give cyclones a counterclockwise circulation in the Northern Hemisphere. In the Southern Hemisphere, cyclones tend to circulate in the clockwise direction.