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with a cyan wheel and a yellow low-density plastic arm undergoes continuous rotation. Its offset geometry drives the arm along a circular trajectory. A cyan backpack is connected at the distal end of the arm. As the crank rotates, the arm transmits motion, inducing jerky, intermittent forward translation of the backpack. The backpack slides subject to kinetic friction, its displacement strictly coupled to the crank's angular position. Each rotation cycle generates tension in the plastic arm, drawing the backpack forward prior to release. 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A rigid connecting rod links the journal to a red backpack. During crank rotation, the connecting rod transmits motion, inducing jerky and intermittent forward displacement of the backpack. Kinetic friction resists the sliding motion, while displacement remains strictly coupled to the crank's angular position. The yellow arm traverses the cycle, repeatedly pulling the connecting rod. Friction determines the sliding velocity, counteracting vibrational forces generated by the rotating wheel. 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Generation/SinglePhysics/CrankPush__bg244__OurPHw_trajectory/caption.txt b/Leaderboard/Video Generation/SinglePhysics/CrankPush__bg244__OurPHw_trajectory/caption.txt new file mode 100644 index 0000000000000000000000000000000000000000..7561119117271d322eaac86597b33605eefb367d --- /dev/null +++ b/Leaderboard/Video Generation/SinglePhysics/CrankPush__bg244__OurPHw_trajectory/caption.txt @@ -0,0 +1 @@ +An active crank equipped with a red distressed wheel and a reddish-brown reflective arm rotates, driving an eccentric journal along a circular trajectory. A rigid rod connects this journal to a yellow-green backpack traversing the sand surface. Motion transmitted through the rod induces jerky, intermittent forward translation of the backpack. 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A rigid rod connects the journal to a beige matte woven backpack. Upon wheel rotation, the rod transmits motion, resulting in jerky, intermittent forward translational motion of the backpack. 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A rigid rod connects the journal to a teal woven smooth-surface backpack. Rotational motion transmits force through the rigid rod, inducing discontinuous and intermittent forward translation. Dynamic resistance impedes the backpack's motion. 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0000000000000000000000000000000000000000..b1f0ffcbbbe3e274f184c96a7e82e9886b3fdb7f --- /dev/null +++ b/Leaderboard/Video Generation/SinglePhysics/CrankPush__bg244__bHGvuj_trajectory/caption.txt @@ -0,0 +1 @@ +An active crank featuring a salmon-colored wheel and a green arm rotates, driving an offset journal along a circular trajectory. A rigid rod directly connects this journal to a salmon-colored backpack. During crank rotation, the rod transmits motion, resulting in jerky, intermittent forward translation of the backpack. Kinetic resistance opposes the sliding backpack, with its displacement strictly coupled to the crank's angular position. 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A rigid rod connects this journal to a cyan backpack positioned statically on the sand surface. During rotation, the rod transmits force, driving the backpack to undergo jerky, intermittent forward translation. 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0000000000000000000000000000000000000000..1c0e11b304038f5e169594a4c1ab18961fcaa77a --- /dev/null +++ b/Leaderboard/Video Generation/SinglePhysics/CrankPush__bg244__l9AWcT_trajectory/caption.txt @@ -0,0 +1 @@ +An active crank featuring a gray wheel and a pale green swirled arm rotates, driving its eccentric journal along a circular trajectory. A rigid rod connects this rotating mechanism to a cyan backpack. As the crank rotates, the rod transmits force, inducing jerky and intermittent forward rectilinear translation of the backpack. During sliding, the backpack experiences kinetic frictional resistance, and its displacement is strictly coupled to the crank’s angular position. 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A rigid rod connects the moving journal to a red backpack. As the crank rotates, the rod transmits motion, inducing jerky and intermittent forward translation of the backpack across the sand surface. During sliding, the backpack experiences kinetic frictional resistance, and its displacement is strictly coupled to the crank's angular position. 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An eccentric journal on the crank traverses a circular trajectory, pulling the rigid rod attached to the red backpack. Force transmission induces jerky, intermittent forward translational motion of the backpack. While sliding, the backpack encounters kinetic frictional resistance, with displacement strictly coupled to the crank angular position. 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Its eccentric journal traces a circular trajectory. A rigid rod connects this journal to a light yellow-grey backpack situated on the ground. Rotational motion drives the rod, forcing the backpack to undergo jerky, intermittent forward translation along the sandy surface. 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The light propagates toward the first elliptical mirror. At the surface, the ray reflects with an angle of reflection equal to the angle of incidence, in accordance with the law of reflection. The beam propagates linearly to the second elliptical mirror. A second reflection occurs as the path traverses an interlocking tile surface. The optical trajectory maintains consistent angles relative to the normal at each interface. 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Light propagates linearly to the first elliptical mirror, reflecting toward the second elliptical mirror at an angle equal to the angle of incidence. Upon incidence at the second mirror, the beam undergoes secondary reflection, continuing along its path. The trajectory strictly adheres to the law of reflection at each interface, maintaining consistent propagation angles between the two reflective surfaces. The apparatus precisely directs energy, ensuring the optical path is defined by the geometric arrangement of the mirrors rather than external variables. 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sequentially arranged elliptical mirror surfaces. 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The light ray strikes the interface and reflects at an angle equal to the angle of incidence, directed toward a second elliptical mirror. Secondary reflection occurs at the second interface, and the beam propagates linearly across the interlocking tile surface. The trajectory undergoes precise alteration at each contact point, adhering to the law of reflection. Energy is emitted from the source, rebounds from the surfaces, exhibiting no deflection between collisions. 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The angle of reflection equals the angle of incidence as the light propagates toward the second elliptical mirror. Following incidence on the second reflective surface, the beam undergoes secondary reflection, proceeding linearly through interlocking tiles. Each interaction adheres to the law of reflection, ensuring the emergent ray maintains precise angular symmetry relative to the normal. Energy transfers unimpeded between contact points, establishing optical surface alignment and defining geometric trajectories based on the initial emission direction. 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At this interface, the light undergoes reflection wherein the angle of incidence equals the angle of reflection. The beam propagates forward along a rectilinear path arriving at the second elliptical mirror. Here, a second reflection occurs, following optical laws while maintaining a linear trajectory. The beam retains coherence throughout the sequence, altering direction only at the reflective surfaces. Each reflection adheres to the principle that the incident ray, reflected ray, and normal lie in the same plane. 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0000000000000000000000000000000000000000..763bb894c547d785798bb6d16b4259b54dc05763 --- /dev/null +++ b/Leaderboard/Video Generation/SinglePhysics/FixedArrayRedirect__bg299__oNTyQD_trajectory/caption.txt @@ -0,0 +1 @@ +A golden laser pen emits a beam from a device mounted on a yellow-green surface, directed toward the first elliptical mirror. Upon incidence, the light undergoes reflection wherein the angle of reflection equals the angle of incidence, redirecting the path to the second mirror. The light propagates rectilinearly between surfaces, strictly adhering to the law of reflection at each interface. The beam completes a precise double-reflection sequence, maintaining geometric consistency throughout transmission. 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The light reflects symmetrically, propagating to the second elliptical mirror. After impact, it deflects again along a straight path on the interlocking tiles. In each interaction, the equality between the angle of incidence and the angle of reflection relative to the surface normal is preserved. The beam continues to traverse the surfaces, maintaining constant geometric angles at each interface.