Mao Kurata Un Official Fan Site Tribute

Mao Kurata : This Is An Un Official Fan Site Tribute
Mao Kurata
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Movie Title Year Distributor Notes Rev Formats 3 Gals Occupy My House 2015 Kira Kira 4 Abnormal Plays 2012 S1 Charisma Dancer H Cup Pole Dancing 2014 Kira Kira Cowgirl Style Soapland 2014 Moodyz Creampie Fuck on the Beach 2014 Kira Kira Creampie into Cosplayer 2015 Moodyz Creampie Sex Manager 2014 Moodyz Face Shower Debut 2012 S1 Flexible Pako Pako 2013 S1 Four Abnormal Plays 2012 S1 Juicy Love Sex (II) 2012 S1 Luxury Life During Little Expectation of Life 2014 Soft on Demand Molesting Delusion of School Girl 2013 S1 No.1 Style Newcomer: Mao Kurata 2012 S1 Reward Journey for Debut 2012 S1 Sensitive Breast 2013 S1 Slow Hand Job 2015 Moodyz Summer Festival 2014 2014 Kira Kira Super Fuckable Fully Naked Lesbian Battle Dynamite 2017 2017 Rocket LezOnly
where {\displaystyle \times }\times denotes the vector cross product. In other words, the rate of change of P in the stationary frame is the sum of its apparent rate of change in the rotating frame and a rate of rotation {\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {P}}}{\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {P}}} attributable to the motion of the rotating frame. The vector ? has magnitude ? equal to the rate of rotation and is directed along the axis of rotation according to the right-hand rule. Acceleration Newton's law of motion for a particle of mass m written in vector form is: {\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}\ ,}{\boldsymbol {F}}=m{\boldsymbol {a}}\ , where F is the vector sum of the physical forces applied to the particle and a is the absolute acceleration (that is, acceleration in an inertial frame) of the particle, given by: {\displaystyle {\boldsymbol {a}}={\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\ ,}{\boldsymbol {a}}={\frac {\operatorname {d}^{2}{\boldsymbol {r}}}{\operatorname {d}t^{2}}}\ , where r is the position vector of the particle

. By applying the transformation above from the stationary to the rotating frame three times (twice to {\displaystyle {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}}{\displaystyle {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}} and once to {\displaystyle {\frac {\operatorname {d} }{\operatorname {d} t}}\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]}{\displaystyle {\frac {\operatorname {d} }{\operatorname {d} t}}\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]}), the absolute acceleration of the particle can be written as: {\displaystyle {\begin{aligned}{\boldsymbol {a}}&={\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}={\frac {\operatorname {d} }{\operatorname {d} t}}{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}={\frac {\operatorname {d} }{\operatorname {d} t}}\left(\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\\&=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times \left(\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}+2{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\ .\end{aligned}}}{\displaystyle {\begin{aligned}{\boldsymbol {a}}&={\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}={\frac {\operatorname {d} }{\operatorname {d} t}}{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}={\frac {\operatorname {d} }{\operatorname {d} t}}\left(\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times {\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\\&=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times \left(\left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]+{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}+2{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\ .\end{aligned}}} Force The apparent acceleration in the rotating frame is {\displaystyle \left[{\frac {d^{2}{\boldsymbol {r}}}{dt^{2}}}\right]}{\displaystyle \left[{\frac {d^{2}{\boldsymbol {r}}}{dt^{2}}}\right]}. An observer unaware of the rotation would expect this to be zero in the absence of outside forces. However, Newton's laws of motion apply only in the inertial frame and describe dynamics in terms of the absolute acceleration {\displaystyle {\frac {d^{2}{\boldsymbol {r}}}{dt^{2}}}}{\displaystyle {\frac {d^{2}{\boldsymbol {r}}}{dt^{2}}}}. Therefore, the observer perceives the extra terms as contributions due to fictitious forces. These terms in the apparent acceleration are independent of mass; so it appears that each of these fictitious forces, like gravity, pulls on an object in proportion to its mass. When these forces are added, the equation of motion has the form:[14][15][16] {\displaystyle {\boldsymbol {F}}-m{\frac {\operatorname {d} {\boldsymbol {\omega }}}{\operatorname {d} t}}\times {\boldsymbol {r}}-2m{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d} {\boldsymbol {r}}}{\operatorname {d} t}}\right]-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})}{\boldsymbol {F}}-m{\frac {\operatorname {d}{\boldsymbol {\omega }}}{\operatorname {d}t}}\times {\boldsymbol {r}}-2m{\boldsymbol {\omega }}\times \left[{\frac {\operatorname {d}{\boldsymbol {r}}}{\operatorname {d}t}}\right]-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}}) {\displaystyle =m\left[{\frac {\operatorname {d} ^{2}{\boldsymbol {r}}}{\operatorname {d} t^{2}}}\right]\ .}=m\left[{\frac {\operatorname {d}^{2}{\boldsymbol {r}}}{\operatorname {d}t^{2}}}\right]\ . From the perspective of the rotating frame, the additional force terms are experienced just like the real external forces and contribute to the apparent acceleration.[17][18] The additional terms on the force side of the equation can be recognized as, reading from left to right, the Euler force {\displaystyle -m\operatorname {d} {\boldsymbol {\omega }}/\operatorname {d} t\times {\boldsymbol {r}}}{\displaystyle -m\operatorname {d} {\boldsymbol {\omega }}/\operatorname {d} t\times {\boldsymbol {r}}}, the Coriolis force {\displaystyle -2m{\boldsymbol {\omega }}\times \left[\operatorname {d} {\boldsymbol {r}}/\operatorname {d} t\right]}{\displaystyle -2m{\boldsymbol {\omega }}\times \left[\operatorname {d} {\boldsymbol {r}}/\operatorname {d} t\right]}, and the centrifugal force {\displaystyle -m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})}{\displaystyle -m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})}, respectively.[19] Unlike the other two fictitious forces, the centrifugal force always points radially outward from the axis of rotation of the rotating frame, with magnitude m?2r, and unlike the Coriolis force in particular, it is independent of the motion of the particle in the rotating frame. As expected, for a non-rotating inertial frame of reference {\displaystyle ({\boldsymbol {\omega }}=0)}({\boldsymbol \omega }=0) the centrifugal force and all other fictitious forces disappear.[20] Similarly, as the centrifugal force is proportional to the distance from object to the axis of rotation of the frame, the centrifugal force vanishes for objects that lie upon the axis. Absolute rotation The interface of two immiscible liquids rotating around a vertical axis is an upward-opening circular paraboloid. When analysed in a rotating reference frame of the planet, centrifugal force causes rotating planets to assume the shape of an oblate spheroid. Main article: Absolute rotation Three scenarios were suggested by Newton to answer the question of whether the absolute rotation of a local frame can be detected; that is, if an observer can decide whether an observed object is rotating or if the observer is rotating.[21][22] The shape of the surface of water rotating in a bucket. The shape of the surface becomes concave to balance the centrifugal force against the other forces upon the liquid. The tension in a string joining two spheres rotating about their center of mass. The tension in the string will be proportional to the centrifugal force on each sphere as it rotates around the common center of mass. In these scenarios, the effects attributed to centrifugal force are only observed in the local frame (the frame in which the object is stationary) if the object is undergoing absolute rotation relative to an inertial frame. By contrast, in an inertial frame, the observed effects arise as a consequence of the inertia and the known forces without the need to introduce a centrifugal force. Based on this argument, the privileged frame, wherein the laws of physics take on the simplest form, is a stationary frame in which no fictitious forces need to be invoked. Within this view of physics, any other phenomenon that is usually attributed to centrifugal force can be used to identify absolute rotation. For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force. The oblate spheroid shape reflects, following Clairaut's theorem, the balance between containment by gravitational attraction and dispersal by centrifugal force. That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation.[23] Applications The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force. For example: A centrifugal governor regulates the speed of an engine by using spinning masses that move radially, adjusting the throttle, as the engine changes speed. In the reference frame of the spinning masses, centrifugal force causes the radial movement. A centrifugal clutch is used in small engine-powered devices such as chain saws, go-karts and model helicopters. It allows the engine to start and idle without driving the device but automatically and smoothly engages the drive as the engine speed rises. Inertial drum brake ascenders used in rock climbing and the inertia reels used in many automobile seat belts operate on the same principle. Centrifugal forces can be used to generate artificial gravity, as in proposed designs for rotating space stations. The Mars Gravity Biosatellite would have studied the effects of Mars-level gravity on mice with gravity simulated in this way. Spin casting and centrifugal casting are production methods that use centrifugal force to disperse liquid metal or plastic throughout the negative space of a mold. Centrifuges are used in science and industry to separate substances. In the reference frame spinning with the centrifuge, the centrifugal force induces a hydrostatic pressure gradient in fluid-filled tubes oriented perpendicular to the axis of rotation, giving rise to large buoyant forces which push low-density particles inward. Elements or particles denser than the fluid move outward under the influence of the centrifugal force. This is effectively Archimedes' principle as generated by centrifugal force as opposed to being generated by gravity. Some amusement rides make use of centrifugal forces. For instance, a Gravitron's spin forces riders against a wall and allows riders to be elevated above the machine's floor in defiance of Earth's gravity.[24] Nevertheless, all of these systems can also be described without requiring the concept of centrifugal force, in terms of motions and forces in a stationary frame, at the cost of taking somewhat more care in the consideration of forces and motions within the system. History of conceptions of centrifugal and centripetal forces Main article: History of centrifugal and centripetal forces The conception of centrifugal force has evolved since the time of Huygens, Newton, Leibniz, and Hooke who expressed early conceptions of it. Its modern conception as a fictitious force arising in a rotating reference frame evolved in the eighteenth and nineteenth centuries.[citation needed] Centrifugal force has also played a role in debates in classical mechanics about detection of absolute motion. Newton suggested two arguments to answer the question of whether absolute rotation can be detected: the rotating bucket argument, and the rotating spheres argument.[25] According to Newton, in each scenario the centrifugal force would be observed in the object's local frame (the frame where the object is stationary) only if the frame were rotating with respect to absolute space. Nearly two centuries later, Mach's principle was proposed where, instead of absolute rotation, the motion of the distant stars relative to the local inertial frame gives rise through some (hypothetical) physical law to the centrifugal force and other inertia effects. Today's view is based upon the idea of an inertial frame of reference, which privileges observers for which the laws of physics take on their simplest form, and in particular, frames that do not use centrifugal forces in their equations of motion in order to describe motions correctly. The analogy between centrifugal force (sometimes used to create artificial gravity) and gravitational forces led to the equivalence principle of general relativity.[26][27] Other uses of the term While the majority of the scientific literature uses the term centrifugal force to refer to the particular fictitious force that arises in rotating frames, there are a few limited instances in the literature of the term applied to other distinct physical concepts. One of these instances occurs in Lagrangian mechanics. Lagrangian mechanics formulates mechanics in terms of generalized coordinates {qk}, which can be as simple as the usual polar coordinates {\displaystyle (r,\ \theta )}(r,\ \theta ) or a much more extensive list of variables.[28][29] Within this formulation the motion is described in terms of generalized forces, using in place of Newton's laws the Euler–Lagrange equations. Among the generalized forces, those involving the square of the time derivatives {(dqk???/?dt?)2} are sometimes called centrifugal forces.[30][31][32][33] In the case of motion in a central potential the Lagrangian centrifugal force has the same form as the fictitious centrifugal force derived in a co-rotating frame.[34] However, the Lagrangian use of "centrifugal force" in other, more general cases has only a limited connection to the Newtonian definition. In another instance the term refers to the reaction force to a centripetal force, or reactive centrifugal force. A body undergoing curved motion, such as circular motion, is accelerating toward a center at any particular point in time. This centripetal acceleration is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with Newton's third law of motion, the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted by the body in curved motion on the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion.[35][36] [37][38] This reaction force is sometimes described as a centrifugal inertial reaction,[39][40] that is, a force that is centrifugally directed, which is a reactive force equal and opposite to the centripetal force that is curving the path of the mass. The concept of the reactive centrifugal force is sometimes used in mechanics and engineering. It is sometimes referred to as just centrifugal force rather than as reactive centrifugal force[41][42] although this usage is deprecated in elementary mechanics

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