📚 OxfordAQA International A Level Mathematics 9660 Mechanics Topic Test | OxfordAQA 国际 A Level 数学 9660 力学专题测试
This revision guide covers the essential mechanics content tested in the OxfordAQA International A Level Mathematics 9660 topic test. It is designed to help you recall key definitions, apply standard models, and avoid common errors under timed conditions.
本复习指南涵盖 OxfordAQA 国际 A Level 数学 9660 力学专题测试中的核心内容，旨在帮助你在限时条件下回忆关键定义、应用标准模型并避免常见错误。
1. Kinematics in One Dimension | 一维运动学
In mechanics, kinematics describes motion without considering the forces that cause it. For straight-line motion, three quantities are fundamental: displacement (s), velocity (v) and acceleration (a).
在力学中，运动学研究运动本身而不考虑产生运动的力。对于直线运动，三个基本量是位移（s）、速度（v）和加速度（a）。
- Displacement is a vector measured in metres (m). — 位移是矢量，单位为米（m）。
- Velocity is the rate of change of displacement, measured in m s⁻¹. — 速度是位移的变化率，单位为 m s⁻¹。
- Acceleration is the rate of change of velocity, measured in m s⁻². — 加速度是速度的变化率，单位为 m s⁻²。
For uniform acceleration there are four standard equations, often called SUVAT equations, because they link s, u, v, a and t.
对于匀加速运动，有四个标准方程，通常称为 SUVAT 方程，因为它们联系 s、u、v、a 和 t。
v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t
These equations work only when acceleration is constant. If acceleration changes with time, you must use differentiation or integration instead.
这些方程仅在加速度恒定时适用。如果加速度随时间变化，你必须改用微分或积分。
2. Using SUVAT Equations | SUVAT 方程的使用
You must choose the SUVAT equation that contains the three known quantities and the unknown you want to find. Write down s, u, v, a and t, fill in the values, and select the equation that avoids the unnecessary variable.
你必须选择包含三个已知量和所要求未知量的 SUVAT 方程。写下 s、u、v、a 和 t，填入数值，并选择避开不需要变量的方程。
| Quantity | Letter | SI unit | 中文 |
|---|---|---|---|
| displacement | s | m | 位移 |
| initial velocity | u | m s⁻¹ | 初速度 |
| final velocity | v | m s⁻¹ | 末速度 |
| acceleration | a | m s⁻² | 加速度 |
| time | t | s | 时间 |
The positive direction must be consistent. If upward is positive, then gravity is a = −9.8 m s⁻². If downward is positive, then gravity is a = +9.8 m s⁻².
正方向必须一致。如果向上为正，重力加速度为 a = −9.8 m s⁻²。如果向下为正，重力加速度为 a = +9.8 m s⁻²。
For example, a particle accelerates from rest at 2 m s⁻² for 5 s. The final velocity is found from v = u + at: v = 0 + 2 × 5 = 10 m s⁻¹.
例如，一个质点从静止开始以 2 m s⁻² 的加速度运动 5 s。末速度由 v = u + at 求得：v = 0 + 2 × 5 = 10 m s⁻¹。
3. Projectile Motion | 抛体运动
A projectile moves under gravity alone, so the horizontal and vertical components of motion are independent. Horizontal velocity is constant, while vertical motion has constant acceleration g.
抛体仅在重力作用下运动，因此水平和竖直方向的运动相互独立。水平速度恒定，而竖直运动具有恒定加速度 g。
If a particle is projected with speed u at angle θ to the horizontal, the components are:
如果质点以速度 u 与水平方向成 θ 角抛出，其分量为：
x = u cos θ × t
y = u sin θ × t − ½gt²
The time of flight is found from the vertical displacement returning to zero, and the horizontal range uses this time with the constant horizontal speed.
飞行时间由竖直位移回到零求得，水平射程则利用该时间与恒定水平速度计算。
At the highest point, the vertical component of velocity is zero, but the horizontal component remains u cos θ throughout the flight.
在最高点，速度的竖直分量为零，但水平分量在整个飞行过程中始终保持为 u cos θ。
4. Forces and Newton’s Laws | 力与牛顿定律
Newton’s three laws govern all force problems. The resultant force on a particle is the vector sum of all forces; if the particle is in equilibrium, the resultant is zero.
牛顿三大定律支配所有力的问题。作用在质点上的合力是所有力的矢量和；如果质点处于平衡状态，合力为零。
- Newton’s First Law: a body remains at rest or moves with constant velocity unless acted on by a resultant force. — 第一定律：除非受到合力作用，物体保持静止或匀速直线运动。
- Newton’s Second Law: F = ma. — 第二定律：F = ma。
- Newton’s Third Law: action and reaction are equal and opposite. — 第三定律：作用力与反作用力大小相等、方向相反。
F = ma
The unit of force is the newton (N), where 1 N = 1 kg m s⁻². Always convert mass to kilograms and acceleration to m s⁻² before applying this law.
力的单位是牛顿（N），其中 1 N = 1 kg m s⁻²。在应用该定律之前，务必先将质量换算为千克、加速度换算为 m s⁻²。
5. Connected Particles and Tension | 连接体与张力
For connected particles, draw a separate force diagram for each particle. Apply F = ma to each particle along the direction of motion, and treat the string as light and inextensible unless told otherwise.
对于连接体，为每个质点单独画受力图。沿运动方向对每个质点应用 F = ma，除非另有说明，将绳子视为轻绳且不可伸长。
For a particle hanging vertically, the equation is typically T − mg = ma. For a particle on a smooth horizontal table, the equation becomes T = ma.
对于竖直悬挂的质点，方程通常为 T − mg = ma。对于放在光滑水平桌面上的质点，方程变为 T = ma。
T − mg = ma
T = ma
Because the string is inextensible, both particles have the same acceleration; because it is light, tension is the same throughout the string.
由于绳子不可伸长，两个质点具有相同的加速度；由于绳子质量轻，绳中各点张力相同。
6. Friction and Inclined Planes | 摩擦与斜面
The maximum static friction is F = μR, where R is the normal reaction and μ is the coefficient of friction. Kinetic friction is usually assumed to have the same limiting value in simple models.
最大静摩擦力为 F = μR，其中 R 是法向反作用力，μ 是摩擦系数。在简单模型中，动摩擦通常假设具有相同的极限值。
F = μR
On an inclined plane, resolve weight into components parallel and perpendicular to the slope: mg sin θ down the plane, mg cos θ perpendicular to the plane.
在斜面上，将重力分解为平行和垂直于斜面的分力：沿斜面向下的 mg sin θ，垂直斜面的 mg cos θ。
R = mg cos θ
F = mg sin θ
Friction always opposes relative motion or the tendency to move. Draw it in the direction opposite to the possible sliding motion.
摩擦力总是阻碍相对运动或运动趋势。作图时应将摩擦力画在与可能滑动方向相反的一侧。
7. Moments and Equilibrium | 力矩与平衡
The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force. The unit is the newton metre (N m).
力对某点的力矩等于力的大小与从该点到力作用线的垂直距离的乘积。单位是牛顿米（N m）。
Moment = F × d
For a body in equilibrium, the vector sum of forces is zero and the sum of moments about any point is zero.
刚体平衡时，力的矢量和为零，且对任意点的合力矩为零。
- ΣF = 0 — 合力为零。
- ΣM = 0 — 对任意点的合力矩为零。
When drawing a moment problem, mark the pivot clearly and take clockwise moments as positive or negative consistently. Reversing the sign convention midway is a common source of error.
在画力矩问题时，要明确标出支点，并一致地规定顺时针力矩为正或负。中途改变正负号规定是常见的错误来源。
8. Momentum and Impulse | 动量与冲量
Momentum is the product of mass and velocity, p = mv. Impulse is the change in momentum and equals the force applied multiplied by the time for which it acts.
动量是质量与速度的乘积，p = mv。冲量是动量的变化量，等于作用力乘以作用时间。
p = mv
Impulse = F × t = mv − mu
In collisions and explosions, the total momentum is conserved if no external force acts on the system. Always assign a positive direction before writing down velocities.
在碰撞和爆炸中，如果系统不受外力作用，则总动量守恒。在写出速度之前，务必先规定正方向。
For example, a particle of mass 2 kg moving at 5 m s⁻¹ is brought to rest. The impulse is 2 × 0 − 2 × 5 = −10 N s, so the impulse has magnitude 10 N s opposite to the motion.
例如，质量为 2 kg、以 5 m s⁻¹ 运动的质点在停止时，冲量为 2 × 0 − 2 × 5 = −10 N s，因此冲量大小为 10 N s，方向与运动方向相反。Published by TutorHao | Mathematics Revision Series | aleveler.com
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