GCSE CIE Physics: Circular Motion Key Points | GCSE CIE 物理：圆周运动考点精讲

📚 GCSE CIE Physics: Circular Motion Key Points | GCSE CIE 物理：圆周运动考点精讲

Circular motion is a fundamental concept in GCSE CIE Physics, appearing everywhere from satellites orbiting Earth to a car taking a bend. Understanding the key principles, formulas, and force analyses is essential for success in your exams. This revision guide breaks down the topic into clear, bite-sized sections with paired English–Chinese explanations.

圆周运动是 GCSE CIE 物理的一个基本概念，从绕地卫星到转弯的汽车，随处可见。掌握核心原理、公式和受力分析对考试成功至关重要。这份考点精讲将整个主题拆分成清晰的小节，并配以中英双语解释。

1. Definition of Uniform Circular Motion | 匀速圆周运动的定义

Uniform circular motion refers to the movement of an object along a circular path at a constant speed. The word ‘uniform’ indicates that the magnitude of the velocity (the speed) does not change, even though the direction of motion is changing continuously.

匀速圆周运动是指物体以恒定速率沿圆形轨迹运动。’匀速’一词表示速度的大小（速率）保持不变，尽管运动方向在不断改变。

In physics, ‘velocity’ is a vector quantity, so it has both magnitude and direction. Because the direction is always changing in circular motion, the velocity is not constant – the object is accelerating.

在物理学中，’速度’是矢量，既有大小又有方向。由于圆周运动中方向始终在变，速度并不是恒定的——物体具有加速度。

2. Constant Speed but Changing Velocity | 速率恒定但速度变化

In uniform circular motion, the instantaneous velocity vector is always tangent to the circle. Since the tangent line points in a different direction at every point along the path, the velocity direction is forever changing. This continuous change in velocity means the object experiences an acceleration.

在匀速圆周运动中，瞬时速度矢量始终沿轨迹的切线方向。由于不同位置的切线方向不同，速度方向不断改变。这种持续的速度变化意味着物体在加速。

The acceleration is directed towards the centre of the circle and is called centripetal acceleration. It is always perpendicular to the velocity, which is why it alters the direction but not the speed.

加速度指向圆心，称为向心加速度。它始终与速度垂直，因此只改变运动方向而不改变速率大小。

If the centripetal force required to keep the object in the circle suddenly disappears, the object will move off along the tangent in a straight line at constant speed, obeying Newton’s first law.

若维持圆周运动所需的向心力突然消失，物体将沿切线方向做匀速直线运动，这符合牛顿第一定律。

3. Period and Frequency | 周期与频率

The period (T) is the time it takes for the object to complete one full revolution. Its SI unit is the second (s). Frequency (f) is the number of complete revolutions per second, measured in hertz (Hz).

周期 (T) 是物体完成一整圈旋转所需的时间，国际单位是秒 (s)。频率 (f) 是每秒完成的完整圈数，单位为赫兹 (Hz)。

Period and frequency are reciprocal quantities: f = 1/T, and T = 1/f. For example, a toy car going around a track 10 times in 5 seconds has a frequency of 2 Hz and a period of 0.5 s.

周期与频率互为倒数：f = 1/T，T = 1/f。例如，一辆玩具车在 5 秒内绕轨道 10 圈，其频率为 2 Hz，周期为 0.5 s。

4. Linear Speed and Angular Speed | 线速度与角速度

The linear speed (v) is the distance travelled along the circular path per unit time. In one period, the distance is the circumference, 2πr. Therefore, the constant speed is:

线速度 (v) 是单位时间内沿圆周通过的路程。一个周期内的路程为圆周长 2πr。因此，恒定速率为：

v = 2πr / T

线速度公式为 v = 2πr / T。

Angular speed (ω) describes how quickly the angle changes. In one period, the angle swept out is 2π radians. Hence:

角速度 (ω) 描述角度变化的快慢。一个周期内转过的角度为 2π 弧度，因此：

ω = 2π / T = 2πf

角速度公式为 ω = 2π / T = 2πf。

Linear speed and angular speed are linked by the radius: v = ωr. If you spin an object at constant angular speed, a point farther from the centre has a greater linear speed.

线速度与角速度通过半径关联：v = ωr。若以恒定角速度旋转物体，离圆心越远的点具有越大的线速度。

5. Centripetal Acceleration | 向心加速度

An object moving in a circle experiences an acceleration towards the centre, called centripetal acceleration. This acceleration is responsible for the continuous change in velocity direction. Its magnitude is given by:

做圆周运动的物体具有指向圆心的加速度，称为向心加速度。该加速度是速度方向不断改变的原因。其大小由下式给出：

a = v² / r

or, expressed in terms of angular speed:

或用角速度表示为：

a = ω²r

向心加速度 a = v² / r 或 a = ω²r。

Since v = ωr, the two forms are equivalent. Notice that for a fixed speed, a smaller radius produces a larger acceleration. Also, doubling the speed quadruples the acceleration due to the square relationship.

因为 v = ωr，两种形式等价。注意，在速率不变时，半径越小，加速度越大；同时，速度加倍会使加速度增至原来的四倍（平方关系）。

In CIE exams, always show the direction of centripetal acceleration towards the centre, not outwards.

在 CIE 考试中，务必将向心加速度的方向标为指向圆心，而非向外。

6. Centripetal Force | 向心力

According to Newton’s second law, a net force is needed to produce an acceleration. For circular motion, this net force must point towards the centre and is called the centripetal force. Its magnitude is obtained by multiplying centripetal acceleration by mass:

根据牛顿第二定律，产生加速度需要净力。对于圆周运动，这个净力必须指向圆心，称为向心力。其大小由向心加速度乘以质量得到：

F = mv² / r

或

F = mω²r

向心力 F = mv² / r = mω²r。

Centripetal force is not a new type of force; it is just the name given to the resultant force that acts towards the centre. It can be provided by tension, friction, gravity, the normal reaction, or a combination of forces.

向心力并不是一种新的作用力，它只是指向圆心的合力之名称。它可以由拉力、摩擦力、重力、支持力或几种力的合力提供。

7. Sources of Centripetal Force | 向心力的来源实例

For a car turning a corner on a flat road, the centripetal force is supplied by the friction between the tyres and the road. If the road is wet or icy, friction decreases and the car may not stay on the circular path.

汽车在水平路面上转弯时，向心力由轮胎与路面间的摩擦力提供。如果路面湿滑或结冰，摩擦力减小，汽车可能无法保持圆周轨迹。

When a rubber bung is whirled on a string, the tension in the string provides the centripetal force. If the string is cut, the bung flies off tangentially.

用绳子抡动橡皮塞时，绳子的拉力提供向心力。若绳子被剪断，橡皮塞将沿切线飞出。

For a satellite orbiting Earth, the gravitational pull of the Earth acts as the centripetal force, constantly pulling the satellite towards the Earth’s centre and keeping it in a curved path.

对于绕地卫星，地球的引力充当向心力，不断将卫星拉向地心，使其保持在弯曲轨道上。

In a vertical roller-coaster loop, at the top of the loop, the centripetal force is provided by the weight of the car plus the normal contact force from the track. If the speed is too low, the normal force becomes zero, and weight alone may not be enough to provide the required centripetal force, causing the car to leave the track.

在过山车的竖直圆环顶部，向心力由车厢的重力与轨道支持力共同提供。如果速度过低，支持力为零，仅靠重力可能不足以提供所需的向心力，导致车厢脱离轨道。

8. Analysing Horizontal Circular Motion Problems | 水平圆周运动受力分析

When solving circular motion problems at GCSE level, the key is to identify all forces acting towards the centre and sum them to equal mv²/r. Draw a clear free-body diagram and label each force. For a car on a flat bend, the horizontal component of static friction must equal mv²/r; the normal force balances the weight.

解决 GCSE 水平的圆周运动问题时，关键是识别所有指向圆心的力，并将其总和设置为 mv²/r。画清晰的受力分析图并标注每个力。对于在水平弯道上的汽车，静摩擦力的水平分量必须等于 mv²/r；而支持力平衡重力。

A conical pendulum (a mass on a string moving in a horizontal circle) is another classic example. The string’s tension has a vertical component that balances the weight, and a horizontal component directed towards the centre that provides the centripetal force.

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GCSE CIE Physics: Circular Motion Key Points | GCSE CIE 物理：圆周运动 考点精讲