Moments | 力矩

📚 Moments | 力矩

Moments are central to the study of turning effects in Edexcel A Level Physics. A force applied at a distance from a pivot can cause rotation, and understanding moments allows you to analyse everything from a simple see-saw to cranes, levers and bridge supports.

力矩是 Edexcel A Level 物理中研究转动效应的核心内容。力在距支点一定距离处作用时会产生转动，理解力矩能帮助你分析从简单跷跷板到起重机、杠杆和桥梁支撑等各种问题。

1. Defining a Moment | 力矩的定义

A moment is the turning effect produced by a force acting about a pivot or axis. It is a vector quantity in Edexcel Physics, although at A Level you will usually work with its magnitude and assign clockwise or anticlockwise sense.

力矩是力绕支点或轴产生的转动效应。在 Edexcel 物理中它是矢量，但在 A Level 阶段通常处理大小并判断顺时针或逆时针方向。

moment = force × perpendicular distance from pivot to line of action

The distance used must be the perpendicular distance from the pivot to the line of action of the force, not simply the distance along the object. If a force acts through the pivot, this perpendicular distance is zero and the moment is zero.

所用距离必须是从支点到力的作用线的垂直距离，而不是沿物体的距离。如果力的作用线通过支点，垂直距离为零，力矩也为零。

The SI unit is the newton metre (N m). Do not confuse N m with the joule: a joule is N m as energy, while the moment unit is written N m to show force × distance in a turning context.

国际单位是牛·米 (N m)。不要把 N m 与焦耳混淆：焦耳作为能量也是 N m，而力矩单位写作 N m 表示转动情境下的力×距离。

2. Calculating Moments | 力矩的计算

To calculate a moment accurately, identify the pivot, draw the force arrow, then measure d perpendicular to that arrow. It is often useful to resolve the force into components or extend the line of action.

准确计算力矩时要确定支点，画力的箭头，然后垂直于该箭头测量距离 d。通常将力分解为分力或延长力的作用线很有用。

M = F × d

If the force is not perpendicular to the object, use M = F × d sin θ, where θ is the angle between the force vector and the object or lever arm. Edexcel questions often require you to find the perpendicular component F sin θ.

如果力不垂直于物体，则使用 M = F × d sin θ，其中 θ 是力矢量与物体或力臂之间的夹角。Edexcel 题目经常要求你找出垂直分力 F sin θ。

Always state whether the moment is clockwise or anticlockwise around the chosen pivot. In equilibrium problems this sign convention is essential.

始终说明绕所选支点的力矩是顺时针还是逆时针。在平衡问题中这一符号约定至关重要。

3. The Principle of Moments | 力矩原理

For an object in rotational equilibrium, the sum of the clockwise moments about any pivot equals the sum of the anticlockwise moments about that same pivot. This is the principle of moments.

对于处于转动平衡的物体，绕任一支点的顺时针力矩之和等于绕同一支点的逆时针力矩之和。这就是力矩原理。

Σ clockwise moments = Σ anticlockwise moments

This principle is used to find unknown forces or distances in beams, bridges, levers and practical devices. You can take moments about any point, but choosing the point where an unknown force acts eliminates that unknown from the equation.

该原理用于求梁、桥、杠杆和

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