Equilibrium of forces
| English | Chinese | Pinyin |
|---|---|---|
| equilibrium | 平衡 | píng héng |
| principle of moments | 力矩原理 | lì jǔ yuán lǐ |
| clockwise | 顺时针 | shùn shí zhēn |
| anticlockwise | 逆时针 | nì shí zhēn |
| vector triangle | 矢量三角形 | shǐ liàng sān jiǎo xíng |
A balanced see-saw
- Two children balance a see-saw even when they weigh different amounts.
- The lighter one just sits further out.
- Balance is about both forces and their turning effects.
Two conditions for equilibrium 平衡
- A body is in equilibrium when both are true:
- the resultant force is zero, and the resultant moment is zero.
A couple: two equal and opposite forces, a distance apart, producing a torque
Forces in equilibrium
When forces are balanced the resultant is zero — the vectors form a closed loop. Drag the arrows to keep them cancelling.
Select both conditions a body must meet to be in equilibrium.
Equilibrium = zero resultant force and zero resultant moment. A body can be in equilibrium while moving at constant velocity.
A body with zero resultant force must be in equilibrium.
Not necessarily — a couple gives zero resultant force but still turns the body. You also need zero resultant moment.
Principle of moments 力矩原理
- For a body that is not turning: total clockwise 顺时针 moment = total anticlockwise 逆时针 moment (about any point).
At balance, the total clockwise moment equals the total ____ moment.
That is the principle of moments — the two turning effects cancel about any chosen point.
Solving a balance problem
- Take moments about an unknown force, so its moment is zero and it drops out.
- List each force × its perpendicular distance, then set clockwise = anticlockwise.
- Use "resultant force = 0" if you need a second equation.
Upthrust arises because the pressure on the bottom of the object is greater than on the top
A child of weight $200\ \text{N}$ sits $1.5\ \text{m}$ left of a see-saw pivot. What weight, $1.0\ \text{m}$ to the right, balances it?
Clockwise = anticlockwise: $W \times 1.0 = 200 \times 1.5$, so $W = 300\ \text{N}$.
To simplify a moments problem, it is smart to take moments about the point where:
A force acting at the pivot has zero perpendicular distance, so its moment is zero and it drops out of the equation.
The vector triangle 矢量三角形
- Three forces in equilibrium, drawn tip to tail, form a closed triangle.
- Solve it with the sine/cosine rule, or resolve into perpendicular components instead.
Three forces in equilibrium, drawn tip to tail, form a closed triangle.
Yes — if they balance, the three arrows return to the start, making a closed vector triangle.
You've got it
- equilibrium needs both: zero resultant force and zero resultant moment
- principle of moments: clockwise = anticlockwise about any point
- three balanced forces close into a vector triangle