AP Physics 1 Core Concepts Review | AP物理1核心知识点梳理

📚 AP Physics 1 Core Concepts Review | AP物理1核心知识点梳理

This article provides a comprehensive review of the core concepts tested in AP Physics 1, including key equations, definitions, and problem-solving strategies. Mastering these fundamentals is essential for success on the exam.

本文全面梳理 AP 物理 1 考试中的核心概念，包括关键方程、定义和解题策略。掌握这些基础对考试成功至关重要。

1. Kinematics | 运动学

Kinematics describes motion without reference to its causes. The key quantities are displacement (Δx), velocity (v), acceleration (a), and time (t). In AP Physics 1, you must be able to analyze motion in one and two dimensions using graphs and equations.

运动学描述运动而不涉及引起运动的原因。关键量包括位移 (Δx)、速度 (v)、加速度 (a) 和时间 (t)。在 AP 物理 1 中，你必须能够使用图像和方程分析一维和二维运动。

The three fundamental equations for constant acceleration are:

匀加速运动的三个基本方程是：

v = v₀ + at

Δx = v₀t + ½at²

v² = v₀² + 2aΔx

These equations apply only when acceleration is constant. In free fall, a = -g = -9.8 m/s² near Earth’s surface, and the motion can be separated into horizontal and vertical components for projectile problems.

这些方程仅当加速度恒定时适用。在自由落体运动中，地球表面附近 a = -g = -9.8 m/s²，对于抛体问题可将运动分解为水平和竖直分量。

Velocity-time graph: slope = acceleration, area = displacement.
Position-time graph: slope = velocity.

速度-时间图线：斜率 = 加速度，面积 = 位移。
位置-时间图线：斜率 = 速度。

2. Newton’s Laws of Motion | 牛顿运动定律

Newton’s laws form the foundation of classical mechanics. The first law states that an object at rest stays at rest and an object in motion stays in motion with constant velocity unless acted upon by a net external force (inertia). The second law quantifies this: net force equals mass times acceleration.

牛顿定律构成了经典力学的基础。第一定律指出，除非受到净外力的作用，否则静止物体将保持静止，运动物体将保持匀速直线运动（惯性）。第二定律对此进行量化：净力等于质量乘以加速度。

ΣF = ma

The third law states that for every action there is an equal and opposite reaction: forces come in pairs acting on different objects. Free-body diagrams are essential to identify all forces (gravity, normal, tension, friction, applied) and to resolve components along chosen axes.

第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力：力成对出现并作用在不同物体上。受力分析图对于识别所有力（重力、支持力、张力、摩擦力、外加力）并沿选定坐标轴分解分量至关重要。

Static friction: fₛ ≤ μₛN (maximum before slipping).
Kinetic friction: fₖ = μₖN.
Inclined plane: weight component parallel to incline = mg sinθ, normal component = mg cosθ.

静摩擦力：fₛ ≤ μₛN（滑动前的最大值）。
动摩擦力：fₖ = μₖN。
斜面：重力沿斜面的分量 = mg sinθ，垂直斜面的分量 = 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 centripetal acceleration directed toward the center, caused by a net centripetal force.

物体以恒定速率做圆周运动时，会受到指向圆心的向心加速度，由净向心力引起。

a_c = v² / r

F_c = m v² / r

Newton’s law of universal gravitation describes the attractive force between any two masses:

牛顿万有引力定律描述任意两个质量之间的引力：

F_g = G m₁ m₂ / r²

For a satellite in circular orbit, gravitational force provides the centripetal force, which leads to orbital speed v = √(GM/r) and period. Keplers laws are also relevant: the orbit of a planet is an ellipse, equal areas in equal times, and T² ∝ r³.

对于圆形轨道上的卫星，引力提供向心力，由此可得轨道速度 v = √(GM/r) 和周期。开普勒定律也相关：行星轨道为椭圆，相等时间内扫过相等面积，且 T² ∝ r³。

4. Energy | 能量

Work is done when a force causes displacement in the direction of the force: W = F d cosθ. The work-energy theorem states that the net work equals the change in kinetic energy.

当力使物体沿力的方向发生位移时，力做功：W = F d cosθ。动能定理指出，净功等于动能的变化量。

W_net = ΔK = ½ m v² – ½ m v₀²

Kinetic energy (K = ½ m v²) and potential energy (gravitational: U_g = mgh, elastic: U_s = ½ k x²) make up mechanical energy. In the absence of non-conservative forces (like friction), mechanical energy is conserved: K_i + U_i = K_f + U_f.

动能 (K = ½ m v²) 和势能（重力势能：U_g = mgh，弹性势能：U_s = ½ k x²）构成机械能。在没有非保守力（如摩擦力）的情况下，机械能守恒：K_i + U_i = K_f + U_f。

Power is the rate at which work is done:

功率是做功的快慢：

P = W / t = F v cosθ

Conservative forces (gravity, spring) have path-independent work.
Non-conservative forces (friction, air resistance) dissipate mechanical energy as thermal energy.

保守力（重力、弹力）做功与路径无关。
非保守力（摩擦力、空气阻力）将机械能转化为热能。

5. Momentum | 动量

Momentum is the product of mass and velocity: p = m v. Impulse delivered by a net force equals the change in momentum (impulse-momentum theorem).

动量是质量与速度的乘积：p = m v。净力所提供的冲量等于动量的变化（冲量-动量定理）。

J = F Δt = Δp = m v_f – m v_i

In an isolated system, total momentum is conserved. This principle applies to collisions and explosions. Collisions are classified as elastic (kinetic energy conserved) or inelastic (kinetic energy is not conserved; in a perfectly inelastic collision, objects stick together).

在孤立系统中，总动量守恒。此原理适用于碰撞和爆炸。碰撞分为弹性碰撞（动能守恒）和非弹性碰撞（动能不守恒；在完全非弹性碰撞中，物体粘在一起）。

For two-dimensional collisions, momentum is conserved independently along each axis. Use component analysis to set up conservation equations.

对于二维碰撞，动量在每个坐标轴方向分别守恒。使用分量分析建立守恒方程。

6. Simple Harmonic Motion | 简谐运动

Simple harmonic motion (SHM) occurs when the restoring force is proportional to displacement from equilibrium and opposite in direction: F = -k x. The motion is sinusoidal and characterized by amplitude (A), period (T), and frequency (f).

当回复力与偏离平衡位置的位移成正比且方向相反 (F = -k x) 时，物体做简谐运动。该运动是正弦式的，由振幅 (A)、周期 (T) 和频率 (f) 描述。

For a mass-spring system, the period depends on mass and spring constant:

对于弹簧-质量系统，周期取决于质量和劲度系数：

T = 2π √(m / k)

For a simple pendulum with small angles, the period depends on length and gravitational acceleration:

对于小角度单摆，周期取决于摆长和重力加速度：

T = 2π √(L / g)

Energy in SHM fluctuates between kinetic and potential, but total mechanical energy remains constant: E_total = ½ k A². At equilibrium, speed is maximum; at extremes, potential energy is maximum.

简谐运动中的能量在动能和势能之间转换，但总机械能保持不变：E_total = ½ k A²。在平衡位置速率最大；在最大位移处势能最大。

7. Torque and Rotational Motion | 扭矩与旋转运动

Torque is the rotational analogue of force: it depends on the applied force, the lever arm, and the angle:

扭矩是力的转动对应量，取决于外加力、力臂和角度：

τ = r F sinθ

Rotational inertia (I) quantifies resistance to angular acceleration. For a point mass, I = m r²; for common shapes, values are given or derived. Newtons second law for rotation states:

转动惯量 (I) 定量的描述了对角加速度的抵抗程度。对于质点，I = m r²；对于常见形状，其值会给出或可推导。转动形式的牛顿第二定律为：

Στ = I α

Rotational kinetic energy is given by K_rot = ½ I ω². For an object rolling without slipping, v_cm = ω R, and total kinetic energy is the sum of translational and rotational parts.

转动动能表示为 K_rot = ½ I ω²。对于无滑动的滚动，v_cm = ω R，总动能为平动和转动动能之和。

Angular momentum L = I ω is conserved when net external torque is zero. This explains changes in angular speed when moment of inertia changes (e.g., spinning skater pulling arms in).

当净外力矩为零时，角动量 L = I ω 守恒。这解释了当转动惯量改变时角速度的变化（例如旋转的滑冰者收回手臂）。

8. Electric Charge and Electric Force | 电荷与电场力

Electric charge comes in two types: positive and negative. Like charges repel, opposite charges attract. Charge is conserved and quantized in units of e = 1.6 × 10⁻¹⁹ C.

电荷有两种：正电荷和负电荷。同种电荷相斥，异种电荷相吸。电荷守恒，且以 e = 1.6 × 10⁻¹⁹ C 为基本单元量子化。

Coulomb’s law gives the magnitude of the force between two point charges:

库仑定律给出两点电荷之间力的大小：

F = k |q₁ q₂| / r²

where k = 8.99 × 10⁹ N·m²/C². The direction is along the line joining the charges.

其中 k = 8.99 × 10⁹ N·m²/C²。力的方向沿两电荷的连线。

An electric field E = F / q represents the force per unit charge. Field lines point away from positive charges and toward negative charges. The field due to a point charge is E = k q / r².

电场 E = F / q 表示单位电荷所受的力。电场线从正电荷出发指向负电荷。点电荷产生的电场为 E = k q / r²。

9. DC Circuits | 直流电路

Ohm’s law relates voltage (V), current (I), and resistance (R): V = I R. Resistance depends on material, length, cross-sectional area, and temperature.

欧姆定律描述电压 (V)、电流 (I) 和电阻 (R) 的关系：V = I R。电阻取决于材料、长度、截面积和温度。

Power dissipated in a resistor:

电阻的耗散功率：

P = I V = I² R = V² / R

In series circuits, current is the same through all components; total resistance is R_total = R₁ + R₂ + … . In parallel circuits, voltage is the same across each branch; total resistance is found from 1/R_total = 1/R₁ + 1/R₂ + … . Kirchhoff’s loop rule (sum of potential differences around any closed loop is zero) and junction rule (total current into a junction equals total current out) are essential for complex circuits.

在串联电路中，各处电流相同；总电阻为 R_total = R₁ + R₂ + … 。在并联电路中，各支路两端电压相同；总电阻满足 1/R_total = 1/R₁ + 1/R₂ + … 。基尔霍夫回路定则（任意闭合回路中电势差之和为零）和节点定则（流入节点的总电流等于流出节点的总电流）是分析复杂电路的基础。

10. Waves and Sound | 波与声音

A traveling wave transfers energy without transferring matter. The wave speed is related to frequency and wavelength:

行波传递能量而不传递物质。波速与频率和波长的关系为：

v = f λ

For a string, wave speed depends on tension (F_T) and linear mass density (μ): v = √(F_T / μ). Sound waves are longitudinal; in air, the speed is about 340 m/s at room temperature.

对于弦上的波，波速取决于张力 (F_T) 和线密度 (μ) ：v = √(F_T / μ)。声波是纵波；在室温空气中速度约为 340 m/s。

Standing waves form when two identical waves travel in opposite directions. The fixed ends are nodes (no displacement), and open ends are antinodes (maximum displacement). For a string fixed at both ends, the allowed wavelengths are λₙ = 2L/n, and frequencies are fₙ = n v / (2L) with n = 1, 2, 3, … For a tube open at both ends, the same harmonic series applies; for a tube closed at one end, only odd harmonics exist: λₙ = 4L/n (n = 1, 3, 5, …).

驻波由两列完全相同的波沿相反方向传播时形成。固定端点是波节（位移为零），开口端是波腹（位移最大）。对于两端固定的弦，允许的波长为 λₙ = 2L/n，频率为 fₙ = n v / (2L)，其中 n = 1, 2, 3, … 。对于两端开口的管，适用相同的谐波系列；对于一端封闭的管，只存在奇次谐波：λₙ = 4L/n（n = 1, 3, 5, …）。

The Doppler effect occurs when a source or observer moves relative to the medium, shifting the observed frequency. For sound, the observed frequency is f’ = f (v ± v_o) / (v ∓ v_s), with sign conventions depending on relative motion.

当波源或观察者相对于介质运动时，会发生多普勒效应，使观测频率发生偏移。对于声音，观测频率为 f’ = f (v ± v_o) / (v ∓ v_s)，符号习惯取决于相对运动方向。

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AP Physics 1 Core Concepts Review | AP物理1核心知识点梳理