An object in an accelerated frame will usually be compelled to move with the frame by a fictitious force. If this force is applied mechanically to one part of the object, the transmission of this "holding force" through the object will make the object seem to feel accelerational "g-forces" as if it were suspended in a gravitational field.
This serves as an illustration of the manner in which fictitious forces arise from switching to a non-inertial reference frame. Calculations of physical quantities made in any frame give the same answers, but in some cases calculations are easier to make in a non-inertial frame. (In this simple example, the calculations are equally easy in either of the two frames described.)
To consider another example, taking as our reference frame the surface of the rotating earth, centrifugal force reduces the apparent force of gravity by about one part in a thousand, depending on latitude. This is zero at the poles, maximum at the equator.
Another fictitious force that arises in the case of circular motion is the Coriolis force, which is ordinarily visible only in very large-scale motion like the projectile motion of long-range guns or the circulation of the earth's atmosphere. Neglecting air resistance, an object dropped from a 50 m high tower at the equator will fall 7.7 mm eastward of the spot below where it was dropped because of the Coriolis force.
Both the centrifugal and the Coriolis force are needed to explain the motion of distant objects relative to rotating reference frames. Consider a distant star observed from a rotating spacecraft. In the reference frame co-rotating with the spacecraft the distant star appears to rotate around the spacecraft. The apparent motion of the star requires a fictitious centripetal force acting on the star. Just like in the example of the car in circular motion above, the centrifugal force acting on the star has the same magnitude as the centripetal force, but is directed in the opposite direction.
In this case the Coriolis force has twice the magnitude of the centrifugal force and is directed oppositely to the centrifugal force. Centrifuge force is a position-dependent field. The farther from the rotation center, the bigger the force. Coriolis is a speed dependent field. The faster we see a travelling object, the bigger the force. This has to be like this because objects rotating with our frame will feel only the centrifugal force, while objects static on the outside, will move respect to us and will feel the coriolis to compensate the centrifugal force.
Fictitious forces can be considered to do work, provided that they move an object on a trajectory that changes its energy from potential to kinetic. For example, consider a person in a rotating chair holding a weight in his outstretched arm. If he pulls his arm inward, from the perspective of his rotating reference frame he has done work against centrifugal force. If he now lets go of the weight, from his perspective it spontaneously flies outward, because centrifugal force has done work on the object, converting its potential energy into kinetic. From an inertial viewpoint, of course, the object flies away from him because it is suddenly allowed to move in a straight line. This illustrates that the work done, like the total potential and kinetic energy of an object, can be different in a non-inertial frame than an inertial one.
If a region of spacetime is declared to be Euclidean, and effectively free from obvious gravitational fields, then if an accelerated coordinate system is overlaid onto the same region, it can be said that a uniform fictitious field exists in the accelerated frame (we reserve the word gravitational for the case in which a mass is involved). An object accelerated to be stationary in the accelerated frame will "feel" the presence of the field, and they will also be able to see environmental matter with inertial states of motion (stars, galaxies, etc.) to be apparently falling "downwards" in the field along curved trajectories as if the field is real.
In frame-based descriptions, this supposed field can be made to appear or disappear by switching between "accelerated" and "inertial" coordinate systems.
As the situation is modeled in finer detail, using the general principle of relativity, the concept of a frame-dependent gravitational field becomes less realistic. In these Machian models, the accelerated body can agree that the apparent gravitational field is associated with the motion of the background matter, but can also claim that the motion of the material as if there is a gravitational field, causes the gravitational field - the accelerating background matter "drags light". Similarly, a background observer can argue that the forced acceleration of the mass causes an apparent gravitational field in the region between it and the environmental material (the accelerated mass also "drags light"). This "mutual" effect, and the ability of an accelerated mass to warp lightbeam geometry and lightbeam-based coordinate systems, is referred to as frame-dragging.
Frame-dragging removes the usual distinction between accelerated frames (which show gravitational effects) and inertial frames (where the geometry is supposedly free from gravitational fields). When a forcibly-accelerated body physically "drags" a coordinate system, the problem becomes an exercise in warped spacetime for all observers.