原创| 偶尔的想念

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题主所说重力势能与离心势能相加的方法也是可行的,取旋转的杯子为参考系,则杯中水可视为受到离心惯性力作用,力的方向由杯子圆心辐射向外,大小正比于半径。此离心惯性力与重力组成复合势场,易证其等势面为抛物面。取一小段水滴为研究对象,设质量为m,列一个有关支持力、重力、向心力的方程,可以求出正切值,也就是斜率,然后一积分就是轨迹方程了。

Lord said gravitational potential energy with the centrifugal potential energy addition method is feasible, a rotating cup for reference frame, the water in the cup can be regarded as by centrifugal force, the direction of the force by the glass center outward radiation, size is proportional to the radius. This centrifugal inertial force and gravity constitute a composite potential field, which is easily proved to be a paraboloid. Take a short period of the droplets as the research object, put quality as the m, make a equation about the upward force, gravity, centrifugal force, can calculate tangent value, namely the slope, and then an integral is the trajectory equation.

分析水面上一个液滴的受力情况,液滴在一个旋转的非惯性系下处于平衡状态,通过受力分析(重力,惯性力,支持力)计算出液滴所受的来自液面的支持力方向与液滴距离中心轴距离的x的关系,会发现支持力方向恰好是一个二次函数在某点处的法向,而支持力方向正是该处液面的法向,得解。

Analysis on the water a force of the droplet, the droplet under a rotating non inertial system in balance, through force analysis (gravity, inertia, support) to calculate the droplet supportiveness from the liquid surface of direction and distance droplet center distances of the relationship between x will find support direction is a quadratic function at some point in the normal, normal, and support the direction is there the liquid surface solution.

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