Centrifugal force

In Newtonian mechanics, the centrifugal force is an inertial force (also called a 'fictitious' or 'pseudo' force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis passing through the coordinate system's origin and parallel to the axis of rotation. If the axis of rotation passes through the coordinate system's origin, the centrifugal force is directed radially outwards from that axis.The concept of centrifugal force can be applied in rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves, when they are analyzed in a rotating coordinate system. The term has sometimes also been used for the reactive centrifugal force that may be viewed as a reaction to a centripetal force in some circumstances. Centrifugal force is an outward force apparent in a rotating reference frame. It does not exist when a system is described relative to an inertial frame of reference. All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to the airliner, to the surface of the Earth, or even to the Sun. A reference frame that is at rest (or one that moves with no rotation and at constant velocity) relative to the 'fixed stars' is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, and descriptions more intuitive. When this choice is made, fictitious forces, including the centrifugal force, arise. In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to the square of the angular velocity of the frame. This is the centrifugal force. As humans usually experience centrifugal force from within the rotating reference frame, e.g. on a merry-go-round or vehicle, this is much more well-known than centripetal force. Motion relative to a rotating frame results in another fictitious force: the Coriolis force. If the rate of rotation of the frame changes, a third fictitious force (the Euler force) is required. These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts). A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, that is changing direction. If a car is traveling at a constant speed along a straight road, then a passenger inside is not accelerating and, according to Newton's second law of motion, the net force acting on him is therefore zero (all forces acting on him cancel each other out). If the car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling him towards the right. This is the fictitious centrifugal force. It is needed within the passenger's local frame of reference to explain his sudden tendency to start accelerating to the right relative to the car—a tendency which he must resist by applying a rightward force to the car (for instance, a frictional force against the seat) in order to remain in a fixed position inside. Since he pushes the seat toward the right, Newton's third law says that the seat pushes him toward the left. The centrifugal force must be included in the passenger's reference frame (in which the passenger remains at rest): it counteracts the leftward force applied to the passenger by the seat, and explains why this otherwise unbalanced force does not cause him to accelerate. However, it would be apparent to a stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as he must in order to keep moving with the car rather than proceeding in a straight line as he otherwise would. Thus the 'centrifugal force' he feels is the result of a 'centrifugal tendency' caused by inertia. Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is often reported in 'G's'.