Circular Motion

This lesson covers the physics of objects moving in circles, including centripetal force and centripetal acceleration — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to understand why a force is needed for circular motion, what provides that force in different situations, and why velocity changes even when speed is constant.

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Objects Moving in Circles

When an object moves in a circle at constant speed, it might seem like nothing is changing — but its velocity is constantly changing. This is because velocity is a vector quantity (it has both magnitude and direction), and the direction of a moving object in a circle is always changing.

Key Distinction: Speed vs Velocity

Quantity	Type	What It Measures
Speed	Scalar	How fast (magnitude only)
Velocity	Vector	How fast AND in which direction

An object moving in a circle at constant speed has a constantly changing velocity because its direction changes at every point along the circle.

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Centripetal Acceleration

Since the velocity is constantly changing (direction changes), the object is constantly accelerating — even though its speed stays the same. This acceleration is called centripetal acceleration.

Centripetal acceleration is always directed towards the centre of the circle.

Why Towards the Centre?

• At any point on the circle, the object's velocity is directed along the tangent (at right angles to the radius).
• A moment later, the velocity has the same magnitude but a slightly different direction.
• The change in velocity points towards the centre.
• Since acceleration is the rate of change of velocity, the acceleration points towards the centre.

Exam Tip: Do not confuse centripetal acceleration with speeding up. The object is not getting faster — its speed is constant. The acceleration is entirely due to the continuous change in direction. This is a subtle but important distinction.

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Centripetal Force

By Newton's Second Law (F = ma), if there is a centripetal acceleration towards the centre, there must be a resultant force towards the centre causing it. This force is called the centripetal force.

Centripetal force is the resultant force that acts on an object moving in a circle, directed towards the centre of the circle.

Key Points About Centripetal Force

• Centripetal force is not a new type of force — it is always provided by an existing force (gravity, tension, friction, etc.).
• It acts perpendicular to the velocity (towards the centre, while velocity is along the tangent).
• It does not do work on the object (because it is perpendicular to the direction of motion), which is why the speed does not change.
• If the centripetal force is removed, the object moves off in a straight line along the tangent (Newton's First Law).

graph TD
    A["Object Moving in a Circle"] --> B["Velocity: along the<br/>tangent to the circle"]
    A --> C["Centripetal Force: towards<br/>the centre of the circle"]
    A --> D["Centripetal Acceleration:<br/>towards the centre"]
    C --> E["Provided by an<br/>existing force:<br/>gravity, tension,<br/>friction, etc."]
    A --> F["If force removed:<br/>object flies off<br/>in a straight line<br/>(tangent)"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#c0392b,color:#fff
    style D fill:#e67e22,color:#fff
    style E fill:#27ae60,color:#fff
    style F fill:#8e44ad,color:#fff

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What Provides the Centripetal Force?

The centripetal force is provided by different forces in different situations:

Situation	Object Moving in a Circle	Centripetal Force Provided By
Planet orbiting the Sun	Planet	Gravitational force from the Sun
Moon orbiting the Earth	Moon	Gravitational force from the Earth
Satellite orbiting the Earth	Satellite	Gravitational force from the Earth
Car going around a bend	Car	Friction between the tyres and the road
Ball on a string (swung in a circle)	Ball	Tension in the string
Clothes in a spin dryer	Clothes	Normal contact force from the drum
Fairground ride (e.g. spinning chairs)	Rider	Tension in the chains/arms
Electron orbiting a nucleus	Electron	Electrostatic force of attraction

Exam Tip: A common exam question asks you to name the force that provides the centripetal force in a specific situation. Make sure you identify the actual force (gravity, friction, tension, etc.), NOT just "centripetal force." Centripetal force describes the role the force plays, not the type of force.

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Factors Affecting Centripetal Force

The centripetal force required to keep an object moving in a circle depends on three factors:

Factor	Effect on Required Centripetal Force
Increasing mass	Increases the required centripetal force
Increasing speed	Increases the required centripetal force (force ∝ v²)
Decreasing radius	Increases the required centripetal force (tighter circle needs more force)

Practical Examples

• A heavier car needs more friction to go around the same bend at the same speed.
• A car going around a bend faster needs more friction — if the friction is insufficient, the car skids off.
• A tighter bend (smaller radius) requires more centripetal force at the same speed.

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What Happens When the Force Is Removed?

If the centripetal force is suddenly removed (e.g. the string breaks, the road becomes icy), the object no longer has a force pulling it towards the centre. By Newton's First Law, it will continue moving in a straight line in the direction it was travelling at that instant — along the tangent to the circle.

Example: Hammer Throw

An athlete spins a hammer in a circle. When released, the hammer flies off in a straight line tangent to the circle at the point of release. The athlete aims to release at the correct point so the hammer travels in the desired direction.

Example: Car on Icy Road

A car going around a bend relies on friction for centripetal force. If the road is icy (very low friction), there is insufficient centripetal force and the car continues in a straight line — sliding off the road.

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Circular Motion and Gravity: Orbits

For objects in orbit (planets, moons, satellites):