Can you accelerate without changing speed?

At first sight it seems a paradox. We have learnt that acceleration means “change in velocity”. So how can a ball moving at constant speed round a circle be accelerated?

The crux is that velocity is a vector, not a number. Even if its magnitude stays fixed, its direction changes at every instant: the arrow representing $\vec{v}$ rotates continuously to remain tangent to the trajectory. And changing the direction of a vector is changing the vector, even at constant magnitude. Mechanics forces us to take that arrow, and its change of orientation, seriously.

This is not a technical detail. It is why the Moon continually “falls” towards the Earth without ever actually falling: Earth’s gravity does not change the Moon’s speed, but continuously bends its trajectory, deflecting it from the straight line it would follow through inertia. “Constant magnitude” does not mean “zero acceleration” — and this distinction, subtle but decisive, is at the heart of all circular motion.

Try it — interactive simulation

A ball on a rotating disk, held toward the centre by a spring: the required centripetal force grows with angular speed. Increase the rotation and watch the equilibrium radius move outward.

▶ The Most Mind-Blowing Aspect of Circular Motion — All Things Physics

Links

Topics: Dynamics Concepts: Centripetal acceleration · Uniform circular motion

Related exercises: Centripetal acceleration of a point · Why circular motion is accelerated · Derivation of centripetal acceleration