Motion in a Circle | Physics

📖 In-Depth Theory

Speed vs Velocity in Circular Motion

An object moving in a circle at CONSTANT SPEED is still ACCELERATING.

WHY?

VELOCITY is a vector — it has both magnitude (speed) and direction.

In circular motion, the DIRECTION continuously changes even if speed stays constant.

Changing direction → changing velocity → ACCELERATION.

This seems counterintuitive — 'constant speed = no acceleration' is a common error.

For circular motion: speed is constant, but velocity is NOT constant.

CENTRIPETAL ACCELERATION:

The acceleration is always directed towards the CENTRE of the circle.

Centre-seeking = centripetal.

At any point on the circle:

Velocity is TANGENTIAL — at 90° to the radius.

Acceleration (and net force) points towards the CENTRE.

Centripetal Force

Because the object accelerates towards the centre, there must be a NET FORCE towards the centre.

This is the CENTRIPETAL FORCE.

Important: centripetal force is NOT a new type of force — it is the NET INWARD FORCE produced by existing forces.

EXAMPLES of what provides centripetal force:

Planet orbiting Sun: GRAVITY pulls planet towards Sun.

Car on a roundabout: FRICTION between tyres and road.

Ball on a string: TENSION in the string.

Electron orbiting nucleus: ELECTROSTATIC ATTRACTION.

Roller coaster loop at top: NORMAL CONTACT FORCE + GRAVITY.

F_centripetal = mv²/r (not required at GCSE but useful context).

WHAT HAPPENS IF THE CENTRIPETAL FORCE IS REMOVED:

Ball on string: string cuts → ball flies off tangentially (not outward — tangentially).

This is Newton's 1st Law: without force, object continues in straight line.

Orbits and Circular Motion

For an ORBIT at constant speed:

Gravitational force provides centripetal force.

The orbit is stable when gravitational pull exactly provides the centripetal force needed.

If SPEED INCREASES (at same orbit radius):

Centripetal force needed = mv²/r → increases.

Gravity unchanged → less than centripetal force needed → object spirals outward.

For a STABLE ORBIT at greater speed:

Radius must DECREASE — smaller orbit compensates for higher speed.

For a STABLE ORBIT at slower speed:

Radius must INCREASE — larger orbit.

This explains why satellites in lower orbits move FASTER than those in higher orbits.

GEOSTATIONARY SATELLITES:

Specific radius where orbital speed matches Earth's rotation period.

Radius: ~36,000 km.

Faster satellite: needs smaller radius to remain stable.

Slower satellite: needs larger radius.

⚠️ Common Mistake

An object in circular motion at constant SPEED is NOT in equilibrium — it IS accelerating (velocity changes direction). The centripetal force is NOT a separate force — it is the net resultant of existing forces (gravity, tension, friction etc.) directed towards the centre. If the centripetal force is removed, the object moves in a STRAIGHT LINE tangentially — not outward.

📌 Key Note

Circular motion: constant speed, changing velocity (direction changes) → acceleration towards centre. Centripetal force = net inward force (gravity/tension/friction provides it). Remove centripetal force → straight-line tangential motion. Faster orbit at same radius = spiral outward; stable faster orbit needs smaller radius.

🎯 Matching Activity — Circular Motion

Match each situation to what provides the centripetal force. — drag the symbols on the right to match the component names on the left.

Planet orbiting the Sun

Drop here

Car going around a roundabout

Drop here

Ball on a string in horizontal circle

Drop here

Satellite in orbit

Drop here

Tension in the string, directed towards the centre

Gravitational attraction of the Sun towards the centre

Gravity pulling satellite towards Earth — no engine needed for stable orbit

Friction between tyres and road surface, directed inward

⭐ Higher Tier Only

HT only — explain why changing direction means acceleration even at constant speed. Identify what provides centripetal force in different situations. Explain orbital stability in terms of speed and radius relationship.

🔬 Triple Science Only

Motion in a circle (HT only) — part of the physics-only extended forces and space physics content.

🎯 Test Yourself

Question 1 of 2

1. A satellite orbits Earth at constant speed. Is it accelerating? Explain.

2. A satellite's orbital speed is increased. What must happen for it to remain in a stable orbit?

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⚡ Motion in a Circle

Speed vs Velocity in Circular Motion

Centripetal Force

Orbits and Circular Motion

Mr. Badmus AI