Year 13 AQA Engineering: Essential Formulas & Theorems Quick-Reference | AQA 工程必考公式定理速查

📚 Year 13 AQA Engineering: Essential Formulas & Theorems Quick-Reference | AQA 工程必考公式定理速查

This handbook compiles the essential formulas, theorems, and principles required for the Year 13 AQA Engineering examination. Each section is carefully organised to reinforce your understanding and provide a rapid reference tool for last-minute revision.

本手册汇编了 Year 13 AQA 工程考试所需的必备公式、定理与原理。各部分精心编排，帮助巩固理解，并为考前冲刺提供速查工具。

1. Statics & Equilibrium | 静力学与平衡

For a body to be in static equilibrium, the vector sum of all forces acting on it must be zero, and the sum of the moments about any point must also be zero.

物体处于静态平衡时，所有作用力的矢量和必须为零，且对任一点的合力矩也须为零。

∑ F = 0, ∑ M = 0

A moment is the turning effect of a force, calculated as the product of the force and the perpendicular distance from the pivot to the line of action of the force.

力矩是力的转动效应，等于力的大小与支点到力作用线的垂直距离的乘积。

M = F d

Forces can be resolved into perpendicular components. Using angle θ with the horizontal, the horizontal component is Fx = F cosθ, and the vertical component is Fy = F sinθ.

力可分解为正交分量。若与水平方向夹角为 θ，则水平分量 Fx = F cosθ，垂直分量 Fy = F sinθ。

Fx = F cos θ, Fy = F sin θ

2. Kinematics of Constant Acceleration | 匀加速运动学

When acceleration is constant, motion can be described using the SUVAT equations, which relate displacement s, initial velocity u, final velocity v, acceleration a, and time t.

加速度恒定时，运动可用 SUVAT 方程描述，这些方程关联位移 s、初速度 u、末速度 v、加速度 a 和时间 t。

Equation 1 (without displacement): final velocity is initial velocity plus acceleration multiplied by time.

方程1（不含位移）：末速度等于初速度加上加速度与时间的乘积。

v = u + a t

Equation 2 (without final velocity): displacement equals initial velocity times time plus one-half acceleration times time squared.

方程2（不含末速度）：位移等于初速度乘以时间，加上二分之一加速度乘以时间的平方。

s = u t + ½ a t²

Equation 3 (without time): the square of final velocity equals the square of initial velocity plus twice the acceleration times displacement.

方程3（不含时间）：末速度的平方等于初速度的平方加上两倍的加速度与位移的乘积。

v² = u² + 2 a s

Equation 4 (without acceleration): displacement equals the average of initial and final velocity multiplied by time.

方程4（不含加速度）：位移等于初速度与末速度的平均值乘以时间。

s = ½ (u + v) t

3. Dynamics, Newton’s Laws & Momentum | 动力学、牛顿定律与动量

Newton’s Second Law states that the resultant force acting on an object is equal to the rate of change of its linear momentum. For a constant mass system, this simplifies to F = m a.

牛顿第二定律指出，物体所受合力等于其线动量的变化率。对质量恒定的系统，可简化为 F = m a。

F = m a

Linear momentum p is a vector quantity defined as the product of an object’s mass and its velocity.

线动量 p 为矢量，定义为物体质量与速度的乘积。

p = m v

The impulse-momentum theorem states that the impulse of a force equals the change in momentum: F t = Δp = m(v – u).

冲量-动量定理表明，力的冲量等于动量的变化：F t = Δp = m(v – u)。

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