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Forces and conservation laws for motion on our spheroidal Earth
American Journal of Physics ( IF 0.9 ) Pub Date : 2021-08-19 , DOI: 10.1119/10.0004801
Boyd F. Edwards 1 , John M. Edwards 2
Affiliation  

We explore the forces and conservation laws that govern the motion of a hockey puck that slides without friction on a smooth, rotating, self-gravitating spheroid. The earth's oblate spheroidal shape (apart from small-scale surface features) is determined by balancing the gravitational forces that hold it together against the centrifugal forces that try to tear it apart. The earth achieves this shape when the apparent gravitational force on the puck, defined as the vector sum of the gravitational and centrifugal forces, is perpendicular to the earth's surface at every point on the surface. Thus, the earth's spheroidal deformations neutralize the centrifugal and gravitational forces on the puck, leaving only the Coriolis force to govern its motion. Motion on the spheroid therefore differs profoundly from motion on a rotating sphere, for which the centrifugal force plays a key role. Kinetic energy conservation reflects this difference: On a stably rotating spheroid, the kinetic energy is conserved in the rotating frame, whereas on a rotating sphere, it is conserved in the inertial frame. We derive these results and illustrate them using CorioVis software for visualizing the motion of a puck on the earth's spheroidal surface.

中文翻译:

在我们的椭球体地球上运动的力和守恒定律

我们探索控制冰球运动的力和守恒定律,冰球在光滑、旋转、自引力的球体上无摩擦滑动。地球的扁球体形状(除了小尺度的表面特征)是通过平衡将其保持在一起的重力与试图将其分开的离心力来确定的。当圆盘上的表观重力(定义为重力和离心力的矢量和)在表面上的每一点都垂直于地球表面时,地球就形成了这种形状。因此,地球的球体变形抵消了圆盘上的离心力和重力,只剩下科里奥利力来控制它的运动。因此,椭球体上的运动与旋转球体上的运动截然不同,其中离心力起着关键作用。动能守恒反映了这种差异:在稳定旋转的球体上,动能在旋转坐标系中守恒,而在旋转球体上,动能在惯性坐标系中守恒。我们推导出这些结果并使用CorioVis软件,用于可视化地球球体表面上圆盘的运动。
更新日期:2021-08-24
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