Illustrated Physics
physics, drawn
Concept

Centripetal acceleration — where it appears

The acceleration toward the centre required to keep a body moving on a circle, equal to the speed squared over the radius. It is present even at unchanging speed, because the velocity's direction is changing — which is why turning is an acceleration and a passenger feels it.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as uniform circular motion — the same set of essays touches all of them, so they are one junction rather than several.

Velocity and acceleration in uniform circular motion. Velocity drawn tangent to a circular path and acceleration drawn toward its centre, at eight points around the circle. The speed never changes and the acceleration is never zero; the two vectors are perpendicular everywhere.

Turning is an acceleration, and constant speed does not help

An object going round a circle at unchanging speed is accelerating hard, all the time, toward a point it never reaches. The construction that shows this needs two arrows and no calculus.

mechanics · Circular motion The deflection is a circle, not a bend. Trajectories integrated from Newton's law in a rotating frame with the Coriolis term and nothing else — no pressure gradient, no friction, no force of any kind. 0.5 m/s at 45°, 0.3 m/s at 30°. Each path closes on itself after one inertial period, checked to a millionth of its own radius, and the radius is the speed divided by the Coriolis parameter: 4.85 km, 4.11 km. The deflection usually described as a curving of the path is a complete circle, traversed clockwise in the northern hemisphere in half a pendulum day, and a body left alone in a rotating frame goes nowhere at all.

The deflection that closes on itself

The Coriolis term is usually described as bending a path to the right. Integrated rather than described, it does not bend the path — it closes it. A body left alone in a rotating frame travels a circle of radius U/f and comes back to where it started in half a pendulum day, having gone nowhere at all, and drifting buoys in every ocean draw exactly that.

mechanics · Circular motion

Named alongside it

The objects these essays reach for when they reach for this one.

Rotating frameUniform circular motionAngular velocityBanked turnBeta planeConservation lawsCoriolis forceFictitious forceFoucault pendulumFree-body diagramFree fallInertial oscillation

All concepts