📚 IB & OCR Physics: Calculation Practice Drills | IB OCR 物理：计算题专项训练
Mastering calculation problems is the backbone of success in both IB and OCR Physics. This article provides a focused set of drills covering essential formulas, unit checks, and common pitfalls. You will build confidence in applying the right equation, handling significant figures, and converting between units under exam pressure.
掌握计算题是 IB 和 OCR 物理取得高分的关键。本文提供一系列专项训练，涵盖核心公式、单位检查与常见陷阱。通过练习，你将能够自信地选用正确方程、处理有效数字并在考试压力下熟练转换单位。
1. Unit & Dimensional Analysis | 单位与量纲分析
Always verify that your final answer has correct SI units. Dimensional analysis helps catch algebraic mistakes before you plug in numbers. For example, if you derive a speed and end up with units of m·s or kg·m·s⁻¹, you know something is wrong.
始终检查最终答案是否具有正确的国际单位。量纲分析能在代入数字前发现代数错误。例如，若你推导出的速度单位是 m·s 或 kg·m·s⁻¹，就说明出错了。
- Write down units for every quantity in an equation.
- 写出方程中每个物理量的单位。
- Treat units as algebraic symbols that can be multiplied, divided, or cancelled.
- 将单位视为可以相乘、相除或约分的代数符号。
Pressure = Force / Area → Pa = N / m² = kg·m⁻¹·s⁻²
2. Kinematic Equations & Graphs | 运动学方程与图像分析
For constant acceleration in a straight line, the SUVAT equations are your toolkit. Always define a positive direction and check the sign of each quantity. The equations are: v = u + at, s = ut + ½at², v² = u² + 2as, and s = ½(u + v)t.
对匀加速直线运动，SUVAT 方程是你的工具箱。务必定义正方向并检查每个量的正负。这些方程为：v = u + at、s = ut + ½at²、v² = u² + 2as 和 s = ½(u + v)t。
- Use the equation that does not require the unknown you are trying to find.
- 使用不包含所求未知量的方程。
- Interpret the gradient of a displacement–time graph as velocity, and the area under a velocity–time graph as displacement.
- 理解位移–时间图像的斜率代表速度，速度–时间图像下的面积代表位移。
3. Newton’s Laws & Free-Body Diagrams | 牛顿定律与受力分析
Newton’s second law, Fnet = ma, must be applied after identifying all forces. Draw a free-body diagram, resolve forces into perpendicular components, and write equations for each axis. Friction is often f = μN, where N is the normal reaction.
应用牛顿第二定律 Fnet = ma 前，必须先识别所有力。画出受力分析图，将力正交分解，并对每个轴列出方程。摩擦力通常为 f = μN，其中 N 是法向反作用力。
- In equilibrium, net force and net torque are zero.
- 在平衡状态下，合力和合力矩均为零。
- For connected bodies, treat the whole system to find acceleration, then examine individual parts for internal forces.
- 对于连接体，先分析整体求加速度，再隔离分析各部分求内力。
4. Work, Energy & Power | 功、能与功率
The work–energy theorem links force, displacement, and speed. Kinetic energy is Ek = ½mv², and gravitational potential energy near Earth’s surface is Ep = mgh. Power is the rate of doing work: P = W/t = Fv for constant velocity.
功能定理将力、位移和速度联系起来。动能为 Ek = ½mv²，地表附近的重力势能为 Ep = mgh。功率是做功的快慢：匀速时 P = W/t = Fv。
- In the absence of non-conservative forces, mechanical energy is conserved.
- 在无非保守力的情况下，机械能守恒。
- Always use metres for extension x in Eelastic = ½kx².
- 在弹性势能 Eelastic = ½kx² 中，伸长量 x 必须用米作单位。
5. Momentum & Impulse | 动量与冲量
Momentum p = mv is a vector. Impulse equals the change in momentum: J = FΔt = Δp. In collisions, use conservation of momentum, but remember kinetic energy is only conserved in perfectly elastic collisions.
动量 p = mv 是矢量。冲量等于动量的变化：J = FΔt = Δp。碰撞问题中应用动量守恒，但切记只有完全弹性碰撞中动能才守恒。
- For two-body explosions or collisions in one dimension: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
- 对于一维两体爆炸或碰撞：m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂。
- The sign of velocity must reflect direction; choose a positive reference and stick to it.
- 速度的正负必须反映方向；选定一个正方向并始终沿用。
6. Circular Motion & Gravitation | 圆周运动与万有引力
Uniform circular motion requires a centripetal force: F = mv²/r = mω²r, where v = ωr and ω = 2π/T. Gravitation provides this force for orbits: F = Gm₁m₂/r².
匀速圆周运动需要向心力：F = mv²/r = mω²r，其中 v = ωr、ω = 2π/T。在轨道运动中，万有引力充当向心力：F = Gm₁m₂/r²。
- For a satellite, equate GmM/r² = mv²/r to derive v = √GM/r.
- 对于卫星，令 GmM/r² = mv²/r 可推出 v = √GM/r。
- Centripetal acceleration always points towards the centre, but the tangential speed is constant in uniform circular motion.
- 向心加速度总是指向圆心，但切向速率在匀速圆周运动中保持不变。
7. Electric Circuits & Kirchhoff’s Laws | 电路与基尔霍夫定律
Ohm’s law V = IR applies to ohmic components. Power dissipated is P = IV = I²R = V²/R. Kirchhoff’s current law states that the sum of currents entering a junction equals the sum leaving. Kirchhoff’s voltage law states the sum of emfs equals the sum of p.d.s around a closed loop.
欧姆定律 V = IR 适用于欧姆元件。功率消耗为 P = IV = I²R = V²/R。基尔霍夫电流定律指出流入节点的电流总和等于流出总和。基尔霍夫电压定律指出闭合回路中电动势之和等于电势差之和。
- For resistors in series: Rtotal = R₁ + R₂; in parallel: 1/Rtotal = 1/R₁ + 1/R₂.
- 电阻串联：R总 = R₁ + R₂；并联：1/R总 = 1/R₁ + 1/R₂。
- Include internal resistance r in real batteries: terminal p.d. = ε − Ir.
- 实际电池需计入内阻 r：路端电压 = ε − Ir。
8. Thermal Physics & Gas Laws | 热物理与气体定律
The ideal gas equation is pV = nRT, where T must be in kelvin. The average kinetic energy of a molecule is Ek = (3/2)kBT. In a sealed container, use p₁V₁/T₁ = p₂V₂/T₂ for fixed mass of gas.
理想气体状态方程为 pV = nRT，其中温度必须用开尔文。分子的平均动能为 Ek = (3/2)kBT。对密封容器内的固定质量气体，可用 p₁V₁/T₁ = p₂V₂/T₂。
- When volume is constant, p ∝ T; when pressure is constant, V ∝ T.
- 体积不变时，p ∝ T；压强不变时，V ∝ T。
- Specific heat capacity: Q = mcΔθ; latent heat: Q = mL.
- 比热容：Q = mcΔθ；潜热：Q = mL。
9. Wave Optics & Interference | 波动光学与干涉
Wave speed is v = fλ. For Young’s double-slit experiment, fringe spacing is Δx = λD/d, where D is the distance to the screen and d is the slit separation. Constructive interference occurs when the path difference is nλ.
波速为 v = fλ。杨氏双缝实验中，条纹间距为 Δx = λD/d，其中 D 是屏幕到双缝的距离，d 是缝距。当光程差为 nλ 时发生加强干涉。
- In a diffraction grating, the condition for maxima is d sinθ = nλ.
- 衍射光栅中，极大条件为 d sinθ = nλ。
- Remember to convert all lengths to metres and use consistent units.
- 记住将所有长度换算成米并使用一致的单位。
10. Nuclear Decay & Half-Life | 核衰变与半衰期
Radioactive decay follows the exponential law: N = N₀ e−λt, where activity A = λN. The half-life T½ is related to the decay constant by T½ = ln2/λ.
放射性衰变遵循指数规律：N = N₀ e−λt，活度 A = λN。半衰期 T½ 与衰变常数的关系为 T½ = ln2/λ。
- After n half-lives, the remaining fraction is (½)n.
- 经过 n 个半衰期后，剩余比例为 (½)n。
- Mass–energy equivalence: E = mc², with mass defect in kg and c in m·s⁻¹.
- 质能方程：E = mc²，质量亏损用千克，光速用 m·s⁻¹。
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