It's good to have a vector pointing in the radial direction of length one.

所以引入这么一个模长为 1,方向沿圆心向外辐射的矢量作用很大

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This equation is telling you if you compress it, namely if x is negative, F will be then positive, because it's pushing you outwards.

这个方程告诉我们,如果压缩弹簧,即令 x 为负,F 就为正,因为推力的方向向外

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er is a vector at each point of length one pointing radially away from the center.

r 是一个模长恒为 1 的矢量,方向沿半径向外

耶鲁公开课 - 基础物理课程节选