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

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

Friction between tyres and road surface, directed inward

Gravitational attraction of the Sun towards the centre

⭐ 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