Torque · 力矩
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| torque/tɔːk/ | 力矩 | lì jǔ |
| lever arm/ˈliːvə ɑːm/ | 力臂 | lì bì |
| vector product/ˈvektə ˈprɒdʌkt/ | 矢量积 | shǐ liàng jī |
| net torque/net tɔːk/ | 净力矩 | jìng lì jǔ |
Why a long wrench beats a short one
- A stuck bolt won't budge with a stubby spanner, but a long one cracks it loose easily.
- Same force from your hand -- yet a completely different result.
- The difference is where and how you push relative to the pivot.
- That twisting effect has a name and a formula.
长扳手为什么胜过短扳手
- 卡住的螺栓用短扳手拧不动,用长扳手却能轻松松开。
- 手上用的力一样——结果却完全不同。
- 区别在于你相对枢轴在哪里、如何施力。
- 这种旋转效果有一个名字和一个公式。
Torque is a twist
- Torque 力矩 measures how strongly a force turns something about an axis:
- $r$ is the distance from the axis, $\theta$ the angle between the force and that line.
- More distance, or a more perpendicular push, means more twist.
力矩是一种"扭"
- 力矩衡量一个力绕轴使物体转动的强度:
- $r$ 是到轴的距离,$\theta$ 是力与那条连线之间的夹角。
- 距离更大,或推得更垂直,就意味着更大的扭转。
A $20\ \text{N}$ force pushes perpendicular to a wrench $0.25\ \text{m}$ from the bolt. What torque results (in N·m)? · 一个 $20\ \text{N}$ 的力垂直推压距螺栓 $0.25\ \text{m}$ 的扳手。产生的扭矩是多少（单位：N·m）？
$\tau = rF\sin 90^\circ = 0.25 \times 20 \times 1 = 5\ \text{N}\cdot\text{m}$.
The same $20\ \text{N}$ at $0.25\ \text{m}$ now acts at $30^\circ$ to the wrench. The torque (in N·m)? · 同样的$20\ \text{N}$在$0.25\ \text{m}$处现在作用于扳手$30^\circ$处。扭矩是多少（单位为N·m）？
$\tau = rF\sin 30^\circ = 0.25 \times 20 \times 0.5 = 2.5\ \text{N}\cdot\text{m}$ -- only the perpendicular part counts. · $\tau = rF\sin 30^\circ = 0.25 \times 20 \times 0.5 = 2.5\ \text{N}\cdot\text{m}$ ——只有垂直部分才算数。
The lever arm
- The lever arm 力臂 is the perpendicular distance from the axis to the line of the force.
- Torque equals force times lever arm -- a longer lever arm wins.
- That is exactly why the long wrench works and pushing near the hinge does not.
力臂
- 力臂是从轴到力的作用线的垂直距离。
- 力矩等于力乘以力臂——力臂越长越有利。
- 这正是长扳手管用、而在铰链附近推却不管用的原因。
The perpendicular distance from the axis to the line of a force is called the lever . · 从轴到力的作用线的垂直距离称为杠杆。
Torque = force times lever arm; a longer lever arm gives more torque. · 力矩 = 力 × 力臂；更长的力臂产生更大的力矩。
Torque as a vector
- More fully, torque is a vector product 矢量积 $\vec{\tau} = \vec{r}\times\vec{F}$.
- Its direction lies along the axis, found by the right-hand rule.
- The magnitude is still $rF\sin\theta$.
作为矢量的力矩
- 更完整地说,力矩是一个矢量积 $\vec{\tau} = \vec{r}\times\vec{F}$。
- 它的方向沿着轴,用右手定则确定。
- 大小仍然是 $rF\sin\theta$。
Torque and the principle of moments · 扭矩和力矩原理
Torque is force times distance from the pivot. Balance the turning effects on each side. · 扭矩是力乘以到支点的距离。平衡两侧的转动效应。
Select all · 所有 true statements about torque. · 选择关于力矩的所有正确陈述。
The first two define torque. A force along the radius gives zero · 零 torque, not maximum. · 前两项定义了力矩。沿半径方向的力给出零力矩，而非最大。
Net torque
- The net torque 净力矩 about an axis is the sum of all the torques on the body.
- Counterclockwise and clockwise torques carry opposite signs.
- A push far from the axis and perpendicular to $r$ gives the most torque.
净力矩
- 绕某轴的净力矩是作用在物体上所有力矩之和。
- 逆时针和顺时针的力矩带相反的符号。
- 在离轴远且与 $r$ 垂直处施力,给出最大的力矩。
A force pushing straight toward the axis produces... · 一个沿径向指向轴的力会产生...
With $\theta = 0$, $\sin 0 = 0$, so the torque is zero -- pushing along the radius cannot spin it. · 由于$\theta = 0$，$\sin 0 = 0$，因此扭矩为零——沿半径推动无法使其旋转。
To get the most torque from a fixed force, apply it... · 为了在固定力下获得最大力矩，应将其施加于...
Torque · 力矩 $rF\sin\theta$ is largest for big $r$ and $\theta = 90^\circ$ -- far out and perpendicular. · 力矩$rF\sin\theta$在大的$r$和$\theta = 90^\circ$时最大——位置越远且垂直越好。
You push a door with $10\ \text{N}$ at the handle, $0.8\ \text{m}$ from the hinge, perpendicular to the door.
- Torque: $\tau = rF\sin 90^\circ = 0.8 \times 10 \times 1 = 8\ \text{N}\cdot\text{m}$.
- Push at $30^\circ$ instead and it drops to $0.8 \times 10 \times 0.5 = 4\ \text{N}\cdot\text{m}$.
你在离铰链 $0.8\ \text{m}$ 的门把手处,垂直于门用 $10\ \text{N}$ 推门。
- 力矩:$\tau = rF\sin 90^\circ = 0.8 \times 10 \times 1 = 8\ \text{N}\cdot\text{m}$。
- 如果改为以 $30^\circ$ 推,它降到 $0.8 \times 10 \times 0.5 = 4\ \text{N}\cdot\text{m}$。
Only the perpendicular part of a force makes torque. A push straight toward the axis ($\theta = 0$) gives $\sin 0 = 0$ -- zero torque, no matter how hard you shove. Pushing along the radius does nothing to spin it.
只有力的垂直部分才产生力矩。直直朝向轴的推力($\theta = 0$)给出 $\sin 0 = 0$——零力矩,无论你推得多用力。沿半径方向推不会使它转动。
Torque $\tau = rF\sin\theta$ (or the vector product $\vec{r}\times\vec{F}$) measures a force's turning effect. It equals force times the lever arm (perpendicular distance to the axis). The net torque sums all torques -- push far out and perpendicular for the most twist.
力矩 $\tau = rF\sin\theta$(或矢量积 $\vec{r}\times\vec{F}$)衡量一个力的转动效果。它等于力乘以力臂(到轴的垂直距离)。净力矩是所有力矩之和——在离轴远且垂直处施力才能获得最大扭转。