Year 12 CCEA Engineering Formula & Theorem Quick Reference Handbook | Year 12 CCEA 工程公式定理速查手册

📚 Year 12 CCEA Engineering Formula & Theorem Quick Reference Handbook | Year 12 CCEA 工程公式定理速查手册

This handbook provides a concise reference for the essential formulas and theorems covered in the Year 12 CCEA Engineering curriculum. It is designed to support quick revision and practical application across key topics such as mechanics, materials, fluids, electricity, and thermodynamics.

本手册为 Year 12 CCEA 工程课程中的核心公式与定理提供简明参考，旨在帮助快速复习和实际应用，涵盖力学、材料、流体、电学和热力学等关键主题。

1. Linear Motion | 直线运动学公式

The following equations describe motion with constant acceleration along a straight line, often called the SUVAT equations.

以下方程描述匀加速直线运动，常被称为 SUVAT 方程。

v = u + a t

This gives the final velocity v after time t, where u is initial velocity and a is constant acceleration.

该式给出经过时间 t 后的末速度 v，其中 u 为初速度，a 为恒定加速度。

s = u t + ½ a t²

This calculates the displacement s when acceleration, initial velocity and time are known.

该式计算位移 s，当已知加速度、初速度和运行时间时使用。

v² = u² + 2 a s

Sometimes called the ‘no-time’ equation, it links velocity and displacement without involving time.

此式有时被称为“无时间方程”，它将速度与位移联系起来而无需知道时间。

s = ½ (u + v) t

It expresses displacement as the product of average velocity and time when acceleration is constant.

该式表示位移等于平均速度乘以时间，前提是加速度恒定。

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2. Forces and Newton’s Laws | 力与牛顿运动定律

Newton’s Second Law defines the relationship between net force, mass, and acceleration.

牛顿第二定律定义了合力、质量与加速度之间的关系。

F = m a

A resultant force F acting on a mass m produces an acceleration a in the same direction as the force.

作用在质量 m 上的合力 F 会产生沿力方向的加速度 a。

Weight is the gravitational force acting on a mass: W = m g, where g is the acceleration due to gravity (approximately 9.81 m/s² near Earth’s surface).

重量是作用于质量上的引力：W = m g，其中 g 为重力加速度（地球表面附近约为 9.81 m/s²）。

W = m g

The frictional force f between two surfaces is limited by the product of the coefficient of friction μ and the normal reaction force R.

两表面间的摩擦力 f 极限值等于摩擦系数 μ 与法向反作用力 R 的乘积。

f ≤ μ R

For a system in translational equilibrium, the vector sum of all forces acting on a body is zero: Σ F_x = 0 and Σ F_y = 0.

对于平动平衡的系统，作用在物体上的所有力的矢量和为零：Σ F_x = 0 且 Σ F_y = 0。

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3. Work, Energy and Power | 功、能与功率

Work done by a constant force is the product of the force component along the displacement and the displacement magnitude.

恒力所做的功等于沿位移方向的力分量与位移大小的乘积。

W = F s cos θ

Kinetic energy E_k of a mass m moving at speed v.

质量为 m、速度为 v 的物体的动能 E_k。

E_k = ½ m v²

Gravitational potential energy gained when an object is raised by a vertical height h.

物体被举高垂直高度 h 时增加的重力势能。

E_p = m g h

Power is the rate of doing work. It can be expressed as P = W / t, or as P = F v for a force moving at constant velocity v in the same direction.

功率是做功的速率。可表达为 P = W / t，或者当力与运动方向一致且速度恒定时 P = F v。

P = W / t = F v

Efficiency (η) indicates how well a machine converts input energy into useful output.

效率 (η) 表示机器将输入能量转化为有用输出能量的程度。

η = (Useful output energy / Total input energy) × 100%

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4. Moments and Equilibrium | 力矩与平衡

The moment of a force about a pivot is the product of the force and the perpendicular distance from the pivot to the line of action of the force.

力对支点的力矩是力与支点到力作用线垂直距离的乘积。

M = F × d

For a body in static equilibrium, the total clockwise moment about any point equals the total anticlockwise moment so that the net moment is zero.

对于静力平衡的物体，绕任意点的顺时针力矩总和等于逆时针力矩总和，从而使

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