旋转纸牌轨迹的近似理论计算

Approximate theoretical calculation of the trajectories of rotating cards

从刚体力学和空气动力学的角度,对2020年国际青年物理学家锦标赛的第17题“玩纸牌(Playing Card)”进行了理论分析和一定的实验验证,计算出了一个水平扔出旋转纸牌的轨迹方程,并通过参数分析讨论了纸牌运动的一些规律.研究发现,影响纸牌运动的主要力是下表面的空气阻力,它一方面导致了纸牌的进动,一方面通过进动产生了三个方向的分力,从而影响了纸牌的轨迹.本文最后通过自主设计的纸牌发射器验证了理论的合理性.

From the perspective of rigid body mechanics and aerodynamics,this paper has carried out theoretical analysis and certain experimental verification on the 17th question"Playing Card"of the international Young Physicists Championship 2020(IYPT2020),and worked out a trajectory equation of a rotating card.Some rules of card’s movement are discussed through parameter analysis.It is found that the main force affecting the movement of card is the air resistance on the lower surface,which on the one hand causes the precession of the card,on the other hand,produces the component force in three directions through the precession,thus affecting the trajectory of the card.Finally,this paper verifies the rationality of the theory by a self-designed card launcher.