📚 AP Physics 1: Must-Know Concepts Summary | AP物理1：必考知识点总结
AP Physics 1 covers the foundational principles of classical mechanics, work and energy, momentum, simple harmonic motion, rotational dynamics, basic circuits, and mechanical waves. This article provides a structured overview of the essential concepts tested on the exam, pairing every explanation in English with its Chinese equivalent to support bilingual learners and ensure solid exam preparation.
AP物理1涵盖经典力学、功与能、动量、简谐运动、转动动力学、基础电路和机械波等核心内容。本文以中英双语逐点对应讲解必考知识点，帮助双语学习者建立清晰的物理图像，稳扎稳打备战考试。
1. Kinematics: Motion in One and Two Dimensions | 运动学：一维与二维运动
Kinematics describes how objects move without considering the causes of motion. You must be able to translate between position-time, velocity-time, and acceleration-time graphs, and apply the four kinematic equations for constant acceleration in both horizontal and vertical directions.
运动学研究物体如何运动而不涉及运动的原因。你需要熟练掌握位置–时间、速度–时间和加速度–时间图像的互译，并能运用匀变速运动的四个运动学方程解决水平和竖直方向的问题。
The four kinematic equations are: v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx, and Δx = ½(v + v₀)t. All of these assume constant acceleration. In projectile motion, analyze horizontal and vertical components independently; the vertical motion has constant acceleration due to gravity g = 9.8 m/s² downward, while horizontal velocity remains constant.
四个运动学方程为：v = v₀ + at，Δx = v₀t + ½at²，v² = v₀² + 2aΔx，以及 Δx = ½(v + v₀)t。所有方程均要求加速度恒定。在抛体运动中，水平与竖直分量独立分析：竖直方向受重力加速度 g = 9.8 m/s² 向下恒定作用，水平速度保持不变。
Graph interpretation is crucial. Velocity is the slope of the position-time graph; acceleration is the slope of the velocity-time graph. The area under an acceleration-time graph gives the change in velocity, while the area under a velocity-time graph gives displacement.
图像分析极为关键。速度是位置–时间图的斜率；加速度是速度–时间图的斜率。加速度–时间图下的面积等于速度变化量，速度–时间图下的面积等于位移。
2. Newton’s Laws and Forces | 牛顿定律与受力分析
Newton’s first law states that an object at rest stays at rest and an object in motion stays in constant velocity unless acted upon by a net external force. Newton’s second law is F_net = ma, and Newton’s third law states that forces come in pairs: if object A exerts a force on object B, B exerts an equal and opposite force on A.
牛顿第一定律指出，除非受到净外力作用，物体将保持静止或匀速直线运动状态。牛顿第二定律为 F_net = ma。牛顿第三定律强调力的成对性：若物体 A 对物体 B 施力，则 B 对 A 施加大小相等、方向相反的力。
Free-body diagrams are your primary tool. Identify all forces acting on a single object: weight (mg), normal force, tension, friction, applied forces. Choose a coordinate system, resolve forces into components, and apply ΣF_x = ma_x, ΣF_y = ma_y. For objects in equilibrium, acceleration is zero, so net force is zero.
受力图是你的首要工具。选定一个物体，标出所有受力：重力 (mg)、法向力、张力、摩擦力、外加力。选定坐标系，分解力为分量，然后应用 ΣF_x = ma_x，ΣF_y = ma_y。物体处于平衡状态时加速度为零，因而合力为零。
Friction comes in two types: static friction f_s ≤ μ_s N, which prevents motion; and kinetic friction f_k = μ_k N, which acts when surfaces slide. Remember that static friction can vary up to a maximum, but kinetic friction is constant. On inclines, weight component parallel to the plane is mg sinθ and perpendicular is mg cosθ.
摩擦力分为两种：静摩擦力 f_s ≤ μ_s N，阻止相对运动；滑动摩擦力 f_k = μ_k N，存在于表面相对滑动时。切记静摩擦力可变化至最大值，而滑动摩擦力为定值。在斜面上，重力平行分量为 mg sinθ，垂直分量为 mg cosθ。
3. Circular Motion and Gravitation | 圆周运动与万有引力
An object moving in a circle at constant speed experiences a centripetal acceleration directed toward the center: a_c = v²/r. By Newton’s second law, a net centripetal force must act: F_c = m v²/r. This force is not a new kind of force; it is provided by tension, gravity, normal force, or friction.
物体做匀速圆周运动时，具有指向圆心的向心加速度：a_c = v²/r。根据牛顿第二定律，必有净向心力作用：F_c = m v²/r。向心力并非新型力，它可由张力、重力、法向力或摩擦力提供。
Newton’s law of universal gravitation states that every mass attracts every other mass with a force F_g = G m₁ m₂ / r², where G = 6.67 × 10⁻¹¹ N·m²/kg². The gravitational field (acceleration) at a planet’s surface is g = G M / R². In orbit, gravitational force provides the centripetal force, leading to relationships between orbital speed, period, and radius.
万有引力定律指出任何两质点间存在引力 F_g = G m₁ m₂ / r²，G = 6.67 × 10⁻¹¹ N·m²/kg²。行星表面引力场加速度为 g = G M / R²。在环绕运动中，引力提供向心力，由此可导出轨道速率、周期与半径的关系。
For a satellite in circular orbit, G M m / r² = m v² / r, so v = √(G M / r). The orbital period is T = 2πr / v, leading to Kepler’s third law: T² ∝ r³. Apparent weight in a rotating space station or on a roller coaster is found by analyzing normal forces using circular motion dynamics.
对圆周轨道上的卫星，G M m / r² = m v² / r，得 v = √(G M / r)。轨道周期 T = 2πr / v，导出开普勒第三定律：T² ∝ r³。在旋转空间站或过山车中的视重，需通过圆周运动动力学分析法向力求得。
4. Work, Energy, and Conservation of Energy | 功、能与能量守恒
Work done by a constant force is W = F d cosθ, where θ is the angle between the force and displacement. The work-energy theorem states that the net work equals the change in kinetic energy: W_net = ΔK = ½mv_f² – ½mv_i². Energy is a scalar measured in joules.
恒力做功 W = F d cosθ，θ 为力与位移的夹角。动能定理指出净功等于动能变化量：W_net = ΔK = ½mv_f² – ½mv_i²。能量是标量，单位为焦耳。
Gravitational potential energy near Earth’s surface is U_g = mgh. Elastic potential energy for a spring is U_s = ½k x², where x is displacement from equilibrium. When only conservative forces do work, mechanical energy is conserved: K_i + U_i = K_f + U_f.
地表附近重力势能为 U_g = mgh。弹簧的弹性势能为 U_s = ½k x²，x 为偏离平衡位置的位移。只有保守力做功时，机械能守恒：K_i + U_i = K_f + U_f。
Power is the rate of doing work: P = W / t or P = F v cosθ for constant force and velocity. In problems with non-conservative forces (like friction), the change in mechanical energy equals the work done by non-conservative forces: W_nc = ΔK + ΔU.
功率是做功的快慢：P = W / t 或恒力恒速率下 P = F v cosθ。存在非保守力（如摩擦力）时，机械能的变化量等于非保守力做的功：W_nc = ΔK + ΔU。
5. Momentum and Impulse | 动量与冲量
Linear momentum is p = m v, a vector. Impulse J = F_avg Δt = Δp. This is especially useful for analyzing collisions and explosions. The area under a force-time graph gives the impulse.
线动量 p = m v，是矢量。冲量 J = F_avg Δt = Δp。这在分析碰撞和爆炸时特别有用。力–时间图下的面积即为冲量。
In a closed, isolated system, total momentum is conserved: Σp_initial = Σp_final. This applies to both elastic and inelastic collisions. In elastic collisions, kinetic energy is also conserved. In perfectly inelastic collisions, objects stick together and kinetic energy is not conserved, but momentum is.
在封闭且孤立的系统中，总动量守恒：Σp_initial = Σp_final。这适用于弹性碰撞和非弹性碰撞。在弹性碰撞中，动能也守恒；在完全非弹性碰撞中，物体粘合，动能不守恒，但动量依然守恒。
For two-object interactions, the conservation of momentum in 1D: m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f. For 2D collisions, break momentum into x- and y-components and conserve each independently. The centre of mass velocity remains constant if no net external force acts.
两个物体的一维动量守恒：m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f。对于二维碰撞，将动量分解为 x 和 y 分量，分别守恒。若无净外力作用，质心速度保持不变。
6. Simple Harmonic Motion (SHM) | 简谐运动
SHM occurs when the restoring force is proportional to displacement from equilibrium: F = -k x. This leads to sinusoidal oscillation. The period of a mass-spring system is T = 2π√(m/k), independent of amplitude. For a simple pendulum with small angles, T = 2π√(L/g).
简谐运动发生时的恢复力与偏离平衡位置的位移成正比：F = -k x，产生正弦振荡。弹簧振子的周期 T = 2π√(m/k)，与振幅无关。小角度单摆的周期 T = 2π√(L/g)。
Energy in SHM continuously transforms between kinetic and potential: total energy E = ½kA² = ½mv_max², where A is amplitude. At maximum displacement, energy is all potential; at equilibrium, it is all kinetic. Position, velocity, and acceleration as functions of time: x(t) = A cos(ωt) or x(t) = A sin(ωt), v(t) = -Aω sin(ωt), a(t) = -Aω² cos(ωt), with ω = 2πf = 2π/T.
简谐运动中的能量在动能与势能间持续转化：总能量 E = ½kA² = ½mv_max²，A 为振幅。最大位移处全部为势能，平衡位置处全部为动能。位置、速度、加速度随时间变化：x(t) = A cos(ωt) 或 x(t) = A sin(ωt)，v(t) = -Aω sin(ωt)，a(t) = -Aω² cos(ωt)，其中 ω = 2πf = 2π/T。
7. Rotational Dynamics and Torque | 转动动力学与力矩
Rotational motion mirrors linear motion. Angular displacement θ, angular velocity ω = Δθ/Δt, angular acceleration α = Δω/Δt. For rigid bodies, points at different radii have the same ω but different linear speed v = rω.
转动运动与线运动相对应。角位移 θ，角速度 ω = Δθ/Δt，角加速度 α = Δω/Δt。对于刚体，不同半径处的点具有相同的 ω，但线速度 v = rω 不同。
Torque τ = r F sinθ, where r is the lever arm. The condition for rotational equilibrium is Στ = 0. Newton’s second law for rotation is Στ = I α, where I is the moment of inertia. The moment of inertia depends on mass distribution relative to the axis: I = Σ m r² for point masses, and for common shapes it is given (e.g., solid disk I = ½MR², thin rod about center I = (1/12)ML²).
力矩 τ = r F sinθ，r 为力臂。转动平衡条件为 Στ = 0。转动形式的牛顿第二定律为 Στ = I α，I 为转动惯量。转动惯量取决于质量相对轴的分布：点质量 I = Σ m r²，常见形状的转动惯量由公式给出（如实心圆盘 I = ½MR²，细杆绕中心 I = (1/12)ML²）。
Rotational kinetic energy is K_rot = ½ I ω². For an object rolling without slipping, v = ωR, and total kinetic energy = ½mv² + ½Iω². Angular momentum L = I ω; if net external torque is zero, angular momentum is conserved: I_i ω_i = I_f ω_f.
转动动能 K_rot = ½ I ω²。无滑滚动时 v = ωR，总动能 = ½mv² + ½Iω²。角动量 L = I ω；当净外力矩为零时，角动量守恒：I_i ω_i = I_f ω_f。
8. Electric Charge and DC Circuits | 电荷与直流电路
Electric charge is conserved. Like charges repel, opposites attract. Coulomb’s law gives the force between two point charges: F = k q₁ q₂ / r², with k = 8.99 × 10⁹ N·m²/C². Electric current I = ΔQ/Δt, and for a resistor, Ohm’s law is V = I R.
电荷守恒。同号相斥，异号相吸。库仑定律给出两点电荷间的作用力：F = k q₁ q₂ / r²，k = 8.99 × 10⁹ N·m²/C²。电流 I = ΔQ/Δt，对电阻器有欧姆定律 V = I R。
In series circuits, current is the same through all components; resistances add: R_eq = R₁ + R₂ + … Voltage divides. In parallel circuits, voltage is the same across each branch; the reciprocal of equivalent resistance is 1/R_eq = 1/R₁ + 1/R₂ + … Current divides.
串联电路中各处电流相等；电阻相加：R_eq = R₁ + R₂ + … 电压分压。并联电路各支路电压相等；等效电阻的倒数相加：1/R_eq = 1/R₁ + 1/R₂ + … 电流分流。
Power in circuits: P = I V = I² R = V²/R. Kirchhoff’s loop rule (ΣV = 0 around any closed loop) and junction rule (ΣI_in = ΣI_out) are essential for analyzing more complex circuits, including those with multiple loops or batteries in series and parallel.
电路中的功率：P = I V = I² R = V²/R。基尔霍夫回路定则（闭合回路内 ΣV = 0）和节点定则（ΣI_in = ΣI_out）是分析多回路或串并联电池组电路的关键。
9. Mechanical Waves and Sound | 机械波与声波
Waves transfer energy without transferring matter. Transverse waves have particle displacement perpendicular to wave direction; longitudinal waves (like sound) have displacement parallel. The wave speed v = f λ, where f is frequency and λ is wavelength. For a string, v = √(F_T / μ), where F_T is tension and μ is linear density.
波传递能量而不传递物质。横波的质点振动方向与波传播方向垂直；纵波（如声波）质点振动方向与传播方向平行。波速 v = f λ，f 为频率，λ 为波长。弦上的波速 v = √(F_T / μ)，F_T 为张力，μ 为线密度。
Superposition principle: when two waves meet, displacements add. Standing waves form when incident and reflected waves interfere at specific frequencies. For a string fixed at both ends, standing wave condition is L = n λ/2, n = 1,2,3… The frequencies are f_n = n v/(2L). Nodes are points of zero displacement; antinodes are points of maximum displacement.
叠加原理：两列波相遇时位移相加。当入射波与反射波以特定频率干涉时形成驻波。两端固定的弦，驻波条件为 L = n λ/2，n = 1,2,3… 频率 f_n = n v/(2L)。波节位移为零，波腹位移最大。
Sound waves are longitudinal pressure waves. The perceived pitch depends on frequency. The Doppler effect shifts observed frequency when the source and observer move relative to each other: f’ = f (v ± v_obs) / (v ∓ v_src), where signs depend on direction of motion towards or away.
声波是纵波压力波。音调取决于频率。当声源与观察者相对运动时，多普勒效应改变观测频率：f’ = f (v ± v_obs) / (v ∓ v_src)，符号取决于靠近或远离的运动方向。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导