Year 12 SQA Physics: Quick Reference Handbook of Formulas & Theorems | 苏格兰Year 12 SQA物理公式定理速查手册

📚 Year 12 SQA Physics: Quick Reference Handbook of Formulas & Theorems | 苏格兰Year 12 SQA物理公式定理速查手册

This handbook provides a compact, exam-focused summary of the essential formulas and theorems you will encounter in the Year 12 SQA Physics course. Each section pairs a clear English statement with an equivalent Chinese explanation, and all equations are displayed using Unicode symbols for instant recall. Use this as a rapid revision aid before assessments.

本手册为Year 12 SQA物理课程提供紧凑且紧扣考点的公式与定理速查。每节采用英文陈述与中文解释配对的形式，所有方程均用Unicode符号显示以便快速回顾。可在评估前用作快速复习工具。

1. Kinematics and Projectile Motion | 运动学与抛体运动

The equations of uniformly accelerated motion relate displacement (s), initial velocity (u), final velocity (v), acceleration (a) and time (t).

匀加速运动方程关联位移（s）、初速度（u）、末速度（v）、加速度（a）和时间（t）。

The first kinematic equation: v = u + a t

v = u + a t

第一运动方程：v = u + a t

expresses displacement when initial velocity and acceleration are known: s = u t + ½ a t²

s = u t + ½ a t²

第二方程在已知初速度与加速度时表示位移：s = u t + ½ a t²

The velocity–displacement relation, useful when time is not given: v² = u² + 2 a s

v² = u² + 2 a s

速度–位移关系，在未知时间时有：v² = u² + 2 a s

The average-velocity form of the displacement equation: s = ½ (u + v) t

s = ½ (u + v) t

位移方程的平均速度形式：s = ½ (u + v) t

component is constant and the vertical motion is under uniform acceleration g = 9.8 m s⁻².

对于以速率 u 并与水平成角度 θ 发射的抛体，水平分量恒定，竖直运动在恒定加速度 g = 9.8 m s⁻² 下进行。

Time to reach maximum height: tₚₑₐₖ = u sin θ / g

tₚₑₐₖ = u sin θ / g

到达最高点的时间：tₚₑₐₖ = u sin θ / g

Maximum height reached: H = (u sin θ)² / (2 g)

H = (u sin θ)² / (2 g)

最大高度：H = (u sin θ)² / (2 g)

Horizontal range for level ground: R = (u² sin 2θ) / g

R = (u² sin 2θ) / g

平地上的水平射程：R = (u² sin 2θ) / g

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2. Forces and Newton's Laws | 力与牛顿定律

Newton's second law states that the net force acting on an object equals the product of its mass and acceleration.

牛顿第二定律指出，作用在物体上的合力等于质量与加速度的乘积。

Sum of forces = m a: ΣF = m a

ΣF = m a

合力公式：ΣF = m a

The weight of an object of mass m in a gravitational field of strength g is W = m g.

质量为 m 的物体在重力场强度为 g 中的重量为 W = m g。

W = m g

重量：W = m g

The maximum static friction or kinetic friction is proportional to the normal reaction force R, with coefficient μ.

最大静摩擦力或动摩擦力与法向反作用力 R 成正比，比例系数为 μ。

Frictional force: F_f = μ R (direction opposes motion or impending motion)

F_f = μ R

摩擦力：F_f = μ R（方向与运动或相对运动趋势相反）

For an object in equilibrium, both the resultant force and the resultant moment are zero.

物体平衡时，合外力与合力矩均为零。

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3. Momentum and Impulse | 动量与冲量

Linear momentum p is the product of mass and velocity.

线动量 p 是质量与速度的乘积。

p = m v

动量：p = m v

Impulse is the change in momentum and equals the average force multiplied by the contact time.

冲量等于动量的变化，也等于平均力乘以接触时间。

Impulse: F Δt = Δp = m v – m u

F Δt = Δp = m v – m u

冲量：F Δt = Δp = m v – m u

In any closed system, total momentum before a collision equals total momentum after the collision.

在任何封闭系统中，碰撞前的总动量等于碰撞后的总动量。

Conservation of momentum: m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

动量守恒：m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

For perfectly elastic collisions, kinetic energy is also conserved; for inelastic collisions, it is not.

完全弹性碰撞中动能也守恒；非弹性碰撞中动能不守恒。

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4. Work, Energy and Power | 功、能与功率

Work done by a constant force is the product of force, displacement and the cosine of the angle between them.

恒力所做的功等于力、位移与两者夹角余弦的乘积。

W = F d cos θ

功：W = F d cos θ

Kinetic energy is the energy an object possesses due to its motion.

动能是物体因运动而具有的能量。

E_k = ½ m v²

动能：E_k = ½ m v²

Gravitational potential energy near the Earth's surface depends on height above a reference level.

地球表面附近的重力势能取决于相对于参考水平面的高度。

E_p = m g h

重力势能：E_p = m g h

Power is the rate of doing work or transferring energy.

功率是做功或转移能量的速率。

P = W / t = F v

功率：P = W / t = F v（当力与速度同

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