Turning effects of forces
| English | Chinese | Pinyin |
|---|---|---|
| pivot | 支点 | zhī diǎn |
| centre of gravity | 重心 | zhòng xīn |
| moment | 力矩 | lì jǔ |
| perpendicular distance | 垂直距离 | chuí zhí jù lí |
| line of action | 作用线 | zuò yòng xiàn |
| couple | 力偶 | lì ǒu |
| torque | 力偶矩 | lì ǒu jǔ |
Why the handle is far from the hinge
- A door handle sits as far from the hinges as possible.
- The same push, applied further from the pivot 支点, turns the door more easily.
- Turning effect depends on force and distance.
Centre of gravity 重心
- The whole weight of an object can be treated as acting at one point: its centre of gravity.
- For a uniform, regular shape it sits at the middle.
The moment 力矩 depends on the perpendicular distance 垂直距离 $d$ from the pivot to the line of action 作用线 of the force
Balance the see-saw
Put a weight on each side and slide it in or out. A small weight far from the pivot can balance a big weight close in — the beam is level when force × distance matches on both sides.
Moment of a force
- The moment is $M = F \times d$, where $d$ is the perpendicular distance from the pivot to the force's line of action.
- Unit: $\text{N}\cdot\text{m}$. A moment is clockwise or anticlockwise.
A force of $20\ \text{N}$ acts at a perpendicular distance of $0.50\ \text{m}$ from a pivot. What is the moment?
$M = F \times d = 20 \times 0.50 = 10\ \text{N}\cdot\text{m}$.
Why is a door handle placed far from the hinges?
Moment $= F \times d$. A bigger $d$ means a bigger turning effect for the same force, so the door opens more easily.
Angle matters
- Only the part of the force perpendicular to the arm turns it.
- For a force at angle $\theta$ to an arm of length $r$: $M = Fr\sin\theta$.
Weights on a rule balanced at a pivot — used to test the principle of moments
Only the part of a force perpendicular to the arm contributes to the turning.
Yes — that is why $M = Fr\sin\theta$: $\sin\theta$ picks out the perpendicular part of the force.
A couple 力偶
- A couple is two forces: equal in size, opposite in direction, a distance apart.
- It makes the body turn only — the resultant force is zero, so no straight-line push.
Select all the features of a couple.
A couple is equal, opposite forces a distance apart, giving zero resultant force but a pure turning effect. Same-direction forces are not a couple.
Torque 力偶矩 of a couple
- The torque is $\tau = F \times d$, where $d$ is the distance between the two lines of action.
- It is the same about any point — a special property of couples.
A couple has forces of $5.0\ \text{N}$ with their lines $0.40\ \text{m}$ apart. What is the torque?
$\tau = F \times d = 5.0 \times 0.40 = 2.0\ \text{N}\cdot\text{m}$.
Two equal forces in the same direction are not a couple — they have a resultant force and push the body along.
Two equal forces pointing in the same direction form a couple.
No — a couple needs equal and opposite forces. Same-direction forces have a resultant and push the body along.
You've got it
- moment $M = F \times d$ — use the perpendicular distance to the line of action
- a couple is equal, opposite forces a distance apart: pure turning, torque $\tau = Fd$
- weight acts at the centre of gravity