Why Circular Motion Means Acceleration

• Velocity is a vector. Around the circle the magnitude (speed) stays constant, but the direction is always changing.
• A changing velocity means an acceleration, by definition (lesson 2.1). So the object accelerates even at constant speed.
• The describe-marks for uniform circular motion: velocity and acceleration both have constant magnitude, and the velocity is always perpendicular to the acceleration (9702/41/O/N/25 Q1(a)).

• The vector triangle shows the direction: subtract two nearby velocity vectors and the change Δv points at the centre. That is why the acceleration is called centripetal.

• The resultant force points at the centre, at 90° to the velocity. Its component along the motion is $F\cos 90^\circ = 0$.
• No force component along the motion means no change in speed: the force only turns the velocity.
• The energy version of the same fact: the force is perpendicular to every movement, so it does no work (lesson 5.02), so the kinetic energy and the speed stay constant.

The two-line answer to every “explain why it accelerates” question: the direction of the velocity is changing, so the velocity is changing; acceleration is the rate of change of velocity, and it points toward the centre.