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Movie Title Year Distributor Notes Rev Formats 3 Gals Occupy My House 2015 Kira Kira Big Breast Fashion Model 2014 Fitch JAV Body Violated In Clothes 2014 Moodyz Boin Girl 2014 Soft on Demand Lesbian in Youth 2014 U&K JAV LezOnly Nude Maid Dispatch Center, Big Tits Division, Mao Hamasaki Speaking 2015 Nadeshiko Facial Creampie Nudist Big-Titted Maid Mao Hamasaki 2014 Oppai Creampie Perfect Body: Mao Hamasaki 2013 Soft on Demand Perfect Rape with Clothes 2014 Moodyz Real Naked Lesbian Battle 2 2015 Rocket LezOnly Squirt Summer Festival 2014 2014 Kira Kira Super Fuckable Fully Naked Lesbian Battle Dynamite 2017 2017 Rocket LezOnly Titty Gang Bang 2014 Golden Time JAV 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 which is parallel to the axis of rotation and passing through the coordinate system's origin. If the axis of rotation passes through the coordinate system's origin, the centrifugal force is directed radially outwards from that axis. The magnitude of centrifugal force F on an object of mass m at the distance r from the origin of a frame of reference rotating with angular velocity ? is:
{\displaystyle F=m\omega ^{2}r}{\displaystyle F=m\omega ^{2}r} 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. In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (brown dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame. Contents

1 Introduction 2 Examples 2.1 Vehicle driving round a curve 2.2 Stone on a string 2.3 Earth 2.3.1 Weight of an object at the poles and on the equator 2.3.2 Equatorial railway 3 Derivation 3.1 Time derivatives in a rotating frame 3.2 Acceleration 3.3 Force 4 Absolute rotation 5 Applications 6 History of conceptions of centrifugal and centripetal forces 7 Other uses of the term 8 See also 9 References 10 External links Introduction Centrifugal force is an outward force apparent in a rotating reference frame.[1][2][3] 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.[4] 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.[5][6] 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[7][8] 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).[7] Examples Vehicle driving round a curve 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.[9] 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.[10] Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is often reported in "G's". Stone on a string If a stone is whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is applied by the string (gravity acts vertically). There is a net force on the stone in the horizontal plane which acts toward the center. In an inertial frame of reference, were it not for this net force acting on the stone, the stone would travel in a straight line, according to Newton's first law of motion. In order to keep the stone moving in a circular path, a centripetal force, in this case provided by the string, must be continuously applied to the stone. As soon as it is removed (for example if the string breaks) the stone moves in a straight line. In this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newton's laws of motion. In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by the string is still acting on the stone. If one were to apply Newton's laws in their usual (inertial frame) form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do. The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame. Earth The Earth constitutes a rotating reference frame because it rotates once every 23 hours and 56 minutes around its axis. Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force: the strength and direction of the local "gravity" at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces. However, the fictitious forces can be of arbitrary size. For example, in an Earth-bound reference system, the fictitious force (the net of Coriolis and centrifugal forces) is enormous and is responsible for the sun orbiting around the Earth (in the Earth-bound reference system). This is due to the large mass and velocity of the sun (relative to the Earth). Weight of an object at the poles and on the equator If an object is weighed with a simple spring balance at one of the Earth's poles, there are two forces acting on the object: the Earth's gravity, which acts in a downward direction, and the equal and opposite restoring force in the spring, acting upward. Since the object is stationary and not accelerating, there is no net force acting on the object and the force from the spring is equal in magnitude to the force of gravity on the object. In this case, the balance shows the value of the force of gravity on the object. When the same object is weighed on the equator, the same two real forces act upon the object. However, the object is moving in a circular path as the Earth rotates and therefore experiencing a centripetal acceleration. When considered in an inertial frame (that is to say, one that is not rotating with the Earth), the non-zero acceleration means that force of gravity will not balance with the force from the spring. In order to have a net centripetal force, the magnitude of the restoring force of the spring must be less than the magnitude of force of gravity. Less restoring force in the spring is reflected on the scale as less weight — about 0.3% less at the equator than at the poles.[11] In the Earth reference frame (in which the object being weighed is at rest), the object does not appear to be accelerating, however the two real forces, gravity and the force from the spring, are the same magnitude and do not balance. The centrifugal force must be included to make the sum of the forces be zero to match the apparent lack of acceleration. Note: In fact, the observed weight difference is more — about 0.53%. Earth's gravity is a bit stronger at the poles than at the equator, because the Earth is not a perfect sphere, so an object at the poles is slightly closer to the center of the Earth than one at the equator; this effect combines with the centrifugal force to produce the observed weight difference.[12] Equatorial railway This section possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (May 2019) (Learn how and when to remove this template message) This thought experiment is more complicated than the previous examples in that it requires the use of the Coriolis force as well as the centrifugal force. If there were a railway line running round the Earth's equator, a train moving westward along it fast enough would remain stationary in a frame moving (but not rotating) with the Earth; it would stand still as the Earth spun beneath it. In this inertial frame the situation is easy to analyze. The only forces acting on the train (assuming no wind resistance or other horizontal forces) are its gravity (downward) and the equal and opposite (upward) force from the track. There is no net force on the train and it therefore remains stationary. In a frame rotating with the Earth the train moves in a circular orbit as it travels round the Earth. In this frame, the upward reaction force from the track and the force of gravity on the train remain the same, as they are real forces. However, in the Earth's (rotating) frame, the train is traveling in a circular path and therefore requires a centripetal (downward) force to keep it on this path. Because this uses a rotating frame, the (fictitious) centrifugal force must be applied to the train. This is equal in value to the required centripetal force but acts in an upward direction — the opposite direction to that required. It would seem that there is a net upward force on the train and it should therefore accelerate upward. The resolution to this paradox lies in the fact that the train is in motion with respect to the rotating frame and is subject to (in addition to the centrifugal force) the Coriolis force, which, in this example, acts in the downward direction and is twice as strong as the centrifugal force. Derivation Main article: Rotating reference frame See also: Fictitious force and Mechanics of planar particle motion For the following formalism, the rotating frame of reference is regarded as a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame denoted the stationary frame. Time derivatives in a rotating frame In a rotating frame of reference, the time derivatives of any vector function P of time—such as the velocity and acceleration vectors of an object—will differ from its time derivatives in the stationary frame. If P1 P2, P3 are the components of P with respect to unit vectors i, j, k directed along the axes of the rotating frame (i.e. P = P1 i + P2 j +P3 k), then the first time derivative [dP/dt] of P with respect to the rotating frame is, by definition, dP1/dt i + dP2/dt j + dP3/dt k. If the absolute angular velocity of the rotating frame is ? then the derivative dP/dt of P with

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