Dynamics – Explaining Motion | 动力学：解释运动

📚 Dynamics – Explaining Motion | 动力学：解释运动

Dynamics is the branch of mechanics that explains why objects accelerate, decelerate, or remain at rest. In CIE A Level Physics, dynamics brings together Newton’s three laws, momentum, impulse, and common forces such as friction and drag. Mastering these ideas allows you to predict motion from forces, analyse collisions, and solve connected-body problems.

动力学是力学中解释物体为何加速、减速或保持静止的分支。在 CIE A Level 物理中，动力学将牛顿三大定律、动量、冲量以及摩擦和阻力等常见力结合起来。掌握这些概念后，你就能根据力预测运动、分析碰撞并求解连接体问题。

1. Newton’s Three Laws of Motion | 牛顿三大运动定律

Newton’s first law states that an object remains at rest or moves with constant velocity unless a resultant external force acts on it. This property is called inertia, and it explains why a passenger lurches forward when a car brakes suddenly.

牛顿第一定律指出，除非受到合外力作用，物体将保持静止或匀速直线运动。这一性质称为惯性，它解释了为什么汽车急刹车时乘客会向前倾。

Newton’s second law links resultant force to rate of change of momentum. For constant mass, it reduces to the familiar equation F = ma. Force and acceleration are vectors and must point in the same direction.

牛顿第二定律将合外力与动量的变化率联系起来。对于质量不变的物体，它简化为我们熟悉的公式 F = ma。力和加速度都是矢量，并且方向相同。

F = Δp / Δt = ma

Newton’s third law says that forces always occur in equal and opposite pairs. If body A exerts a force on body B, body B exerts an equal but oppositely directed force on body A. The two forces act on different objects, so they do not cancel.

牛顿第三定律指出，力总是成对出现，大小相等、方向相反。如果物体 A 对物体 B 施加一个力，那么物体 B 也会对物体 A 施加一个大小相等、方向相反的力。这两个力作用在不同物体上，因此不会相互抵消。

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2. Mass, Weight and Inertia | 质量、重量与惯性

Mass is a scalar quantity measuring the amount of matter in a body. Its SI unit is the kilogram. Mass is also a measure of inertia: a larger mass requires a larger resultant force to produce the same acceleration.

质量是标量，表示物体所含物质的多少，其 SI 单位是千克。质量也是惯性大小的量度：质量越大，要产生相同加速度所需的合外力就越大。

Weight is the gravitational force acting on a mass. It is a vector and always points towards the centre of the planet. Near Earth’s surface, weight is given by W = mg, where g is the gravitational field strength, approximately 9.81 m s⁻².

重量是作用在物体质量上的引力。它是矢量，方向总是指向地球中心。在地球表面附近，重量由 W = mg 给出，其中 g 是重力场强度，约为 9.81 m s⁻²。

W = mg

A common misconception is that mass and weight are the same. An astronaut’s mass is unchanged in space, but their weight becomes much smaller when far from a planet.

常见的误区是认为质量和重量相同。宇航员在太空中的质量不变，但他们远离行星时重量会小得多。

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3. Free-Body Diagrams and Resolving Forces | 受力分析与力的分解

A free-body diagram shows all the external forces acting on a single body. Drawing one is the first step in most dynamics problems because it prevents missing forces such as tension, normal reaction, or friction.

受力图（隔离体图）画出作用在单个物体上的所有外力。画受力图是解决大多数动力学问题的第一步，因为它可以避免遗漏张力、法向反作用力或摩擦力等。

Forces can be resolved into perpendicular components. On an inclined plane, the weight W is usually resolved parallel and perpendicular to the slope: W sin θ down the slope and W cos θ perpendicular to the slope.

力可以分解为互相垂直的分量。在斜面上，重力 W 通常分解为沿斜面方向的分量 W sin θ 和垂直于斜面的分量 W cos θ。

W sin θ = component down slope, W cos θ = component normal to slope

If the object is stationary or moving with constant velocity, the vector sum of forces is zero. This equilibrium condition lets you calculate unknown forces such as the normal reaction or frictional force.

如果物体静止或匀速运动，所有力的矢量和为零。这一平衡条件可以用于计算未知力，例如法向反作用力或摩擦力。

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4. Tension, Normal Reaction and Friction | 张力、法向反作用力与摩擦力

Tension is the pulling force transmitted through a string, cable, or rod. It acts away from the object along the line of the string. A light inextensible string has the same tension throughout its length.

张力是通过绳子、缆绳或杆传递的拉力。它沿绳子方向背离物体。轻质且不可伸长的绳子中各点的张力大小相同。

The normal reaction is the contact force perpendicular to a surface. It balances the perpendicular component of weight or other applied forces, unless the surface is accelerating vertically.

法向反作用力是垂直于接触面的接触力。它平衡重力或其他外力的垂直分量，除非接触面本身在竖直方向加速。

Friction opposes relative motion between two surfaces. For sliding, dynamic friction is proportional to the normal reaction: F = μR, where μ is the coefficient of friction. Static friction can vary up to a maximum value.

摩擦力阻碍两个表面之间的相对运动。滑动时，动摩擦力与法向反作用力成正比：F = μR，其中 μ 是摩擦系数。静摩擦力可以在零到最大值之间变化。

F = μR

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5. Drag Forces and Terminal Velocity | 阻力与终端速度

A body moving through a fluid experiences a drag force that increases with speed. At low speeds, drag is often proportional to speed; at higher speeds, it is usually proportional to speed squared.

物体在流体中运动时会受到随速度增大而增大的阻力。低速时，阻力通常与速度成正比；高速时，通常与速度的平方成正比。

A skydiver initially accelerates downward because weight is greater than air resistance. As the skydiver speeds up, drag increases until it equals weight. At this point, the resultant force becomes zero and the skydiver falls at terminal velocity.

跳伞者最初向下加速，因为重力大于空气阻力。随着速度增大，阻力增加，直到与重力相等。此时合外力为零，跳伞者以终端速度下落。

The velocity-time graph of a falling object with drag has an initial near-linear rise, then curves and approaches a horizontal line at terminal velocity. The acceleration decreases from g to zero.

受阻力影响的落体的速度-时间图像最初接近直线上升，然后弯曲并趋近于终端速度的水平线。加速度从 g 逐渐减小到零。

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6. Momentum and Impulse | 动量与冲量

Linear momentum is the product of mass and velocity: p = mv. Momentum is a vector quantity; its direction is the same as the velocity. The SI unit of momentum is kg m s⁻¹.

线动量是质量与速度的乘积：p = mv。动量是矢量，方向与速度相同。动量的 SI 单位是 kg m s⁻¹。

p = mv

Impulse is the product of force and the time for which it acts. According to Newton’s second law, impulse equals the change in momentum: FΔt = Δp. This is especially useful when a force varies over a short time, such as in a kick or collision.

冲量是力与作用时间的乘积。根据牛顿第二定律，冲量等于动量的变化：FΔt = Δp。这在力在短时间内变化的情况（如踢球或碰撞）中特别有用。

Impulse = FΔt = Δ(mv)

On a force-time graph, the impulse is the area under the curve. For a constant force, this is simply a rectangle; for a changing force, the area can be estimated from the graph.

在力-时间图像中，冲量等于曲线下的面积。对于恒力，这是简单的矩形；对于变力，可以通过图像估算面积。

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7. Conservation of Momentum | 动量守恒

The principle of conservation of momentum states that the total momentum of an isolated system remains constant, provided no external resultant force acts. Internal forces, such as those during a collision, occur in equal and opposite pairs and cancel.

动量守恒定律指出，在没有合外力作用的孤立系统中，总动量保持不变。碰撞过程中的内力成对出现，大小相等方向相反，因此彼此抵消。

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