📚 Year 12 CCEA PE: Formula & Theorem Quick Reference Handbook | Year 12 CCEA 体育：公式定理速查手册
This handbook brings together the key formulas and theorems you need for the Year 12 CCEA Physical Education specification. It covers biomechanics, exercise physiology and skill acquisition, providing a clear reference for both learning and exam revision. Use these equations to analyse movement, understand how the body responds to exercise, and explain the science behind performance.
本手册汇集了 Year 12 CCEA 体育课程所需的公式与定理，涵盖生物力学、运动生理学和技能习得领域，是学习与备考的清晰参考。请运用这些方程分析运动、理解身体对运动的反应，并阐释表现背后的科学原理。
1. Linear Motion & Kinematics | 直线运动与运动学
Average speed (v) is the total distance (d) travelled divided by the time (t) taken.
v = d / t
平均速度 (v) 是运动总距离 (d) 除以所用时间 (t)。
Acceleration (a) is the rate of change of velocity. It is calculated as the change in velocity (v – u) divided by the time (t) over which the change occurs.
a = (v – u) / t
加速度 (a) 是速度的变化率。它等于速度变化量 (v – u) 除以发生该变化所用的时间 (t)。
The first SUVAT equation links final velocity (v), initial velocity (u), acceleration (a) and time (t).
v = u + a t
第一个 SUVAT 方程将末速度 (v)、初速度 (u)、加速度 (a) 和时间 (t) 联系起来。
Displacement (s) travelled when accelerating uniformly.
s = u t + ½ a t²
匀加速直线运动的位移 (s)。
The equation linking final velocity, initial velocity, acceleration and displacement without time.
v² = u² + 2 a s
不包含时间的速度–位移关系式。
2. Newton’s Laws of Motion | 牛顿运动定律
Newton’s First Law (inertia): an object remains at rest or moves with constant velocity unless acted upon by an external net force.
牛顿第一定律（惯性定律）：除非受到外力作用，物体将保持静止或匀速直线运动。
Newton’s Second Law describes the relationship between net force (F), mass (m) and acceleration (a).
F = m a
牛顿第二定律描述合外力 (F)、质量 (m) 和加速度 (a) 的关系。
Weight (W or Fg) is the force due to gravity.
W = m g
重力 (W) 即重力的大小。
Newton’s Third Law: for every action, there is an equal and opposite reaction.
牛顿第三定律：作用力与反作用力大小相等、方向相反。
3. Momentum & Impulse | 动量与冲量
Linear momentum (p) is the product of mass (m) and velocity (v).
p = m v
线动量 (p) 为质量 (m) 与速度 (v) 的乘积。
Impulse is the change in momentum, which equals the average force (F) multiplied by the time (Δt) for which it acts.
Impulse = F Δt = Δp = m v – m u
冲量等于动量变化量，等于平均力 (F) 乘以作用时间 (Δt)。
In a closed system, total momentum before collision equals total momentum after collision (conservation of momentum).
m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂
在封闭系统中，碰撞前总动量等于碰撞后总动量（动量守恒）。
4. Forces, Friction & Air Resistance | 力、摩擦与空气阻力
The maximum static frictional force (f) is proportional to the normal reaction force (R) via the coefficient of friction (μ).
f = μ R
最大静摩擦力 (f) 与法向反作用力 (R) 成正比，比例系数为摩擦系数 (μ)。
The drag (air resistance) encountered by a moving body depends on the fluid density (ρ), the velocity (v), the cross‑sectional area (A) and a drag coefficient (Cd).
Fdrag = ½ Cd ρ A v²
运动物体所受空气阻力 (Fdrag) 取决于流体密度 (ρ)、速度 (v)、横截面积 (A) 和阻力系数 (Cd)。
Resultant force is the vector sum of all forces acting on a body. For a skydiver at terminal velocity, weight equals drag, acceleration is zero.
合外力是作用在物体上所有力的矢量和。当跳伞运动员达到终极速度时，重力等于空气阻力，加速度为零。
5. Projectile Motion | 抛体运动
When an object is projected at an angle θ to the horizontal with initial speed v, the horizontal and vertical components of velocity are:
vₓ = v cosθ vy0 = v sinθ
物体以初始速度 v 与水平方向呈 θ 角抛出时，速度的水平分量和竖直分量为：
The horizontal displacement (x) is unaffected by gravity, while vertical displacement (y) is influenced by acceleration due to gravity (g = 9.81 m s⁻²).
x = v cosθ × t y = v sinθ × t – ½ g t²
水平位移 (x) 不受重力影响，竖直位移 (y) 受重力加速度 (g) 影响。
Time of flight for a projectile that lands at the same height:
T = (2 v sinθ) / g
落在同一水平面的抛体飞行时间。
Maximum height reached:
H = (v sinθ)² / (2 g)
最大高度。
Horizontal range (R) is maximised when θ = 45° (neglecting air resistance).
R = (v² sin 2θ) / g
水平射程 (R) 在 θ = 45° 时最大（忽略空气阻力）。
6. Angular Motion & Levers | 角运动与杠杆
Angular velocity (ω) is the rate of change of angular displacement (θ).
ω = Δθ / Δt
角速度 (ω) 是角位移 (θ) 的变化率。
Linear velocity (v) of a point on a rotating body is related to angular velocity and radius (r).
v = r ω
转动体上一点的线速度 (v) 等于半径 (r) 乘以角速度 (ω)。
Centripetal acceleration (ac) points towards the centre of rotation.
ac = v² / r = r ω²
向心加速度 (ac) 指向转动中心。
Torque (τ) is the turning effect of a force, determined by force (F) and its perpendicular distance (d) from the pivot.
τ = F d
力矩 (τ) 是力的转动效应，等于力 (F) 与力到支点的垂直距离 (d) 的乘积。
For a lever system at equilibrium:
Effort × effort arm = Load × load arm
杠杆平衡条件：动力 × 动力臂 = 阻力 × 阻力臂。
7. Fluid Mechanics & Bernoulli Principle | 流体力学与伯努利原理
Bernoulli’s principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy. For streamlined flow:
P + ½ ρ v² + ρ g h = constant
伯努利原理指出，流体流速增加时，压强或势能会减小。对于流线型流动：
The Magnus effect explains how a spinning object (e.g. a football) experiences a sideways force due to pressure differences created by the spin. Faster airflow on one side reduces pressure, generating lift or curve.
马格努斯效应解释旋转物体（如足球）因转速带来的压强差而受到侧向力。流速快的一侧压强低，产生升力或弧线轨迹。
When air moves faster over a curved surface, pressure drops; this is fundamental to the lift on a discus or the swing of a cricket ball.
空气流过曲面时速度加快、压强下降，这是铁饼升力或板球变向的基础原理。
8. Energy, Work & Power | 能量、功与功率
Kinetic energy (Ek) is the energy possessed by a moving object.
Ek = ½ m v²
动能 (Ek) 是运动物体具有的能量。
Gravitational potential energy (Ep) gained when lifting a mass (m) through a height (h).
Ep = m g h
重力势能 (Ep) 等于质量 (m) 提升的高度 (h) 乘以重力加速度 (g)。
Work done (W) when a force (F) moves an object through a displacement (s) at an angle (θ) to the force.
W = F s cosθ
力 (F) 做功 (W) 等于力在位移 (s) 方向的分量乘位移，其中 θ 为力与位移的夹角。
Power (P) is the rate of doing work or the rate of energy transfer.
P = W / t or P
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