📚 Forces and Motion: Newton’s Laws and Applications | 力与运动：牛顿定律及其应用
Understanding forces and motion is central to Cambridge Science. This article reviews the key ideas of speed, acceleration, Newton’s three laws, weight, friction, momentum and energy transfer, with worked-style explanations to support revision.
理解力与运动是剑桥科学课程的核心内容。本文回顾速度、加速度、牛顿三大定律、重力、摩擦力、动量与能量转移等关键概念，并通过典型解释帮助复习。
1. Scalars and Vectors | 标量与矢量
Physical quantities are split into scalars, which have magnitude only, and vectors, which have both magnitude and direction. Distance and speed are scalar quantities, whereas displacement and velocity are vector quantities.
物理量分为标量和矢量：标量只有大小，矢量既有大小又有方向。距离和速率是标量，而位移和速度是矢量。
When describing motion, saying ‘the car travelled 20 km’ gives distance, but saying ‘the car travelled 20 km north’ gives displacement. The direction changes the physical meaning, so vector notation matters in Cambridge exams.
描述运动时，说“汽车行驶了 20 km”给出的是距离，而说“汽车向北行驶了 20 km”给出的是位移。方向改变了物理意义，因此在剑桥考试中矢量表示很重要。
2. Speed and Velocity | 速率与速度
Average speed is the total distance travelled divided by the total time taken. Average velocity is the total displacement divided by the total time taken. The standard equation is:
平均速率是总路程除以总时间。平均速度是总位移除以总时间。标准方程为：
speed = distance ÷ time
If a runner completes a 400 m lap in 50 s, the average speed is 8 m/s, but the average velocity is zero because the start and finish points are the same and displacement is zero.
如果一名跑步者用 50 s 完成一圈 400 m，平均速率为 8 m/s，但平均速度为零，因为起点和终点相同，位移为零。
3. Acceleration | 加速度
Acceleration is the rate of change of velocity. It is a vector and has the SI unit m/s². The equation is:
加速度是速度的变化率。它是矢量，国际单位为 m/s²。方程为：
a = (v − u) ÷ t
where u is initial velocity, v is final velocity and t is the time taken. A negative acceleration is often called deceleration or retardation.
其中 u 是初速度，v 是末速度，t 是所用时间。负加速度通常称为减速度或减速。
4. Newton’s First Law | 牛顿第一定律
Newton’s first law states that an object remains at rest or moves with constant velocity unless acted on by a resultant external force. This property is inertia.
牛顿第一定律指出，除非受到合外力的作用，物体将保持静止或匀速直线运动。这种性质称为惯性。
In a moving car, a passenger lurches forward when the car brakes suddenly because the passenger’s body continues moving forward until the seatbelt provides the unbalanced force to stop it.
在行驶的汽车中，急刹车时乘客会向前倾，因为乘客的身体继续保持向前运动，直到安全带提供不平衡的力使其停止。
5. Newton’s Second Law | 牛顿第二定律
Newton’s second law links resultant force, mass and acceleration:
牛顿第二定律将合外力、质量和加速度联系起来：
F = m × a
where F is the resultant force in newtons (N), m is the mass in kilograms (kg) and a is the acceleration in m/s². A larger force gives a larger acceleration, while a larger mass gives a smaller acceleration for the same force.
其中 F 是合外力，单位为牛顿 (N)；m 是质量，单位为千克 (kg)；a 是加速度，单位为 m/s²。力越大，加速度越大；在相同力作用下，质量越大，加速度越小。
6. Newton’s Third Law | 牛顿第三定律
Newton’s third law states that if body A exerts a force on body B, body B exerts an equal and opposite force on body A. These two forces act on different objects and are the same type.
牛顿第三定律指出，若物体 A 对物体 B 施加一个力，那么物体 B 会对物体 A 施加一个大小相等、方向相反的力。这两个力作用在不同物体上，且属于同种类型。
When a rocket pushes hot gas downwards, the gas pushes the rocket upwards with an equal force, causing upward acceleration. This explains motion in space where there is no ground to push against.
当火箭向下喷出高温气体时，气体以相等的力向上推火箭，使火箭向上加速。这解释了在没有地面可推的太空中的运动。
7. Resultant Forces and Free-Body Diagrams | 合力与受力分析图
The resultant force is the single force that has the same effect as all the individual forces acting on an object. If forces act along the same line, they can be added or subtracted.
合力是能够产生与所有分力相同效果的单个力。如果力沿同一直线作用，可以将它们相加或相减。
For example, a 10 N push to the right and a 4 N friction force to the left give a resultant force of 6 N to the right. The object accelerates to the right according to F = m × a.
例如，向右的 10 N 推力与向左的 4 N 摩擦力产生的合力为向右 6 N。根据 F = m × a，物体将向右加速。
8. Weight and Gravitational Field Strength | 重力与重力场强度
Weight is the force on a mass due to gravity and must not be confused with mass. Weight is calculated by:
重力是质量受到引力作用的力，不能与质量混淆。重力由下式计算：
W = m × g
where W is weight in newtons, m is mass in kg and g is the gravitational field strength. On Earth, g is about 9.81 N/kg, often rounded to 10 N/kg in Cambridge problems.
其中 W 是重力，单位为牛顿；m 是质量，单位为 kg；g 是重力场强度。在地球表面，g 约为 9.81 N/kg，剑桥试题中常取 10 N/kg。
An astronaut’s mass remains the same on the Moon, but their weight is lower because the Moon’s gravitational field strength is only about 1.6 N/kg.
宇航员在月球上的质量不变，但重力较小，因为月球的重力场强度只有约 1.6 N/kg。
9. Friction, Air Resistance and Terminal Velocity | 摩擦力、空气阻力与终极速度
Friction is a force that opposes motion between two surfaces in contact. Air resistance or drag is a type of friction that acts on objects moving through air. The faster an object moves, the greater the drag usually becomes.
摩擦力是阻碍两个接触表面之间运动的力。空气阻力或阻力是物体在空气中运动时受到的一种摩擦力。物体运动越快，阻力通常越大。
When a skydiver first jumps, weight is greater than drag, so the diver accelerates downwards. As speed increases, drag increases until it equals weight. At this point the resultant force is zero and the diver falls at terminal velocity.
跳伞者刚跳下时，重力大于阻力，因此向下加速。随着速度增大，阻力增大，直到等于重力。此时合外力为零，跳伞者以终极速度下落。
10. Momentum | 动量
Momentum is a vector quantity calculated by multiplying mass and velocity:
动量是矢量，等于质量乘以速度：
p = m × v
In a closed system, the total momentum before a collision is equal to the total momentum after the collision. This is the principle of conservation of momentum.
在封闭系统中，碰撞前的总动量等于碰撞后的总动量。这就是动量守恒定律。
Seatbelts and airbags increase the time over which a person’s momentum changes, reducing the force experienced. This is because force is equal to the rate of change of momentum.
安全带和安全气囊延长了人体动量变化的时间，从而减小了受力。这是因为力等于动量的变化率。
11. Work, Energy and Power | 功、能量与功率
Work is done when a force moves an object in the direction of the force. Work is calculated by:
当力使物体沿力的方向移动时，就做了功。功的计算公式为：
W = F × d
where W is work in joules (J), F is the force in newtons and d is the distance moved in metres. Energy is the capacity to do work, and power is the rate of doing work.
其中 W 是功，单位为焦耳 (J)；F 是力，单位为牛顿；d 是移动距离，单位为米。能量是做功的能力，功率是做功的速率。
Power is calculated by:
功率计算公式为：
P = W ÷ t
A machine that does 500 J of work in 10 s has a power output of 50 W.
一台机器在 10 s 内做 500 J 的功，其功率输出为 50 W。
12. Motion Graphs | 运动图像
Distance–time graphs and velocity–time graphs are common in Cambridge science exams. The gradient of a distance–time graph gives speed, while the gradient of a velocity–time graph gives acceleration.
距离–时间图像和速度–时间图像在剑桥科学考试中很常见。距离–时间图像的斜率表示速率，速度–时间图像的斜率表示加速度。
The area under a velocity–time graph gives the displacement. A horizontal line on a velocity–time graph means constant velocity, and a sloping line means uniform acceleration.
速度–时间图像下方的面积表示位移。速度–时间图像上的水平线表示匀速，倾斜线表示匀加速。
- Distance–time graph gradient = speed
- 距离–时间图像斜率 = 速率
- Velocity–time graph gradient = acceleration
- 速度–时间图像斜率 = 加速度
- Velocity–time graph area = displacement
- 速度–时间图像面积 = 位移
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