主要区别-摩擦角与休止角

摩擦角和休止角是机械工程中出现的两个角。休止角在土力学中也有应用。摩擦角和休止角的主要区别在于，摩擦角定义为物体刚开始运动时，法向反作用力与法向反作用力和摩擦力的合力之间的夹角，而休止角定义为使物体从斜面上滑下的斜面的最小角度。我们稍后将看到这两个定义是等价的。

什么是摩擦角(angle of friction)？

摩擦角是指法向反作用力与法向反作用力和摩擦力的合力之间的夹角。让我们首先探讨这个定义，并尝试用公式来表示摩擦角。

Defining angle of friction

The diagram above shows a block being pulled against a rough surface. If the force is **all, the static friction ( ) between the surfaces would prevent the block from moving. If you slowly increase the pull,  would also increase, balancing the horizontal forces and still preventing the block from moving. However, at one point, the block would just begin to move. At this point, the static friction has reached the upper limit, and we can describe this maximum friction as  where  is the coefficient of friction and  is the normal reaction force.

The vector diagram on the right shows the sum of  and  . From the definition we had above,  is the angle of friction. Using trigonometry, we can express this angle  as  . i.e., the angle of friction between two surfaces is equal to the inverse tangent of the coefficient of friction between those two surfaces.

什么是休止角(angle of repose)？

休止角是一个表面可以从水平面倾斜的最大角度，这样它上面的物体就可以停留在表面上而不向下滑动。再一次，让我们先看看形势图。

Defining Angle of Repose

When the object is just about to move, the size of friction is given by  . The object is also in equilibrium (the object is about to move, but it is not moving yet!) so taking the forces acting along the plane, we can say,

.

垂直于平面的分力，

现在，我们取这些表达式的比率：

.

Using the trigonometric identity  , and cancelling out common factors. we get  . So, we get:

For angle of friction , we had and we see that this is the same expression that we get for angle of repose as well. Therefore, angle of friction is equal to angle of repose.

在土力学中，休止角是指一堆土的最浅角度，它使土颗粒开始下落。蚂蚁在建造陷阱时会利用这个角度（见下文）：

Antli*** make these sand traps to catch ants and other **all insects. The sides of these traps are at the angle of repose. When ants wander into the pit, the disturbance causes the sand to begin rolling down, making it difficult for the ant to escape. Then the antlion, which had been hiding at the bottom of the trap, comes out and catches the ant.

摩擦角(angle of friction)和休止角(angle of repose)的区别

基本上，休止角和摩擦角是相同的，由两个表面之间摩擦系数的反切线给出。它们的区别在于描述它们的方式。

描述

摩擦角是物体刚开始沿表面运动时，法向反作用力与摩擦力和法向反作用力的合力之间的夹角。

休止角是斜坡上物体开始向下滑动的最浅角度。

说明适用的地方

摩擦角的定义可以应用于任何类型的表面。

休止角的定义只能在有斜面时使用。

工具书类

班萨尔，R。K(2002). 工程力学教科书。新德里：Laxmi出版物。

Image Courtesy

“sand pit traps of antli*** 2” by Michal Maňas (Own work) [CC BY-SA 2.0], via flickr