12.2 Centripetal Acceleration


2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Understand that a force of constant magnitude that is always perpendicular to the direction of motion causes centripetal acceleration.
  2. Understand that centripetal acceleration causes circular motion with a constant angular speed.
  3. Recall and use a = rω² and a = v²/r.
  4. Recall and use F = mrω² and F = mv²/r.

1. Why Does Circular Motion Need a Force?

Think about what Newton's First Law tells us: an object will keep moving in a straight line at constant speed unless a force acts on it.

So if an object is moving in a circle — constantly changing direction — there must be a force acting on it. Without that force, the object would fly off in a straight line (called a tangent to the circle — a straight line that just touches the circle at one point).

Example: Imagine spinning a ball on a string above your head. The string pulls the ball towards your hand. The moment you let go, the ball flies off in a straight line. The tension in the string was the force keeping it moving in a circle.

Example: The Earth orbits the Sun because gravity pulls the Earth towards the Sun. Without gravity, the Earth would shoot off into space in a straight line.


2. What Is Centripetal Force?

The force that keeps an object moving in a circle is called the centripetal force.

Centripetal force = a resultant (net) force that always points towards the centre of the circle.

The word "centripetal" just means "centre-seeking." It describes the direction of the force, not what type of force it is. The centripetal force can be:

SituationWhat Provides the Centripetal Force
Ball on a stringTension in the string
Earth orbiting the SunGravitational pull of the Sun
Car going round a bendFriction between tyres and road
Electron orbiting a nucleusElectrostatic (electric) force

Important: Centripetal force is not a separate, special type of force. It is simply the name we give to whichever force (or combination of forces) is pointing towards the centre of the circle.

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