Illustrated Physics
physics, drawn
Concept

Uniform circular motion — where it appears

Motion round a circle at unchanging speed, which is accelerated motion throughout because the direction is changing. The acceleration points at the centre and equals the speed squared over the radius, and the construction that shows it needs two arrows and no calculus.

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

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.

Centripetal accelerationRotating frameAngular velocityBanked turnBeta planeConservation lawsCoriolis forceFictitious forceFoucault pendulumFree-body diagramFree fallInertial oscillation

All concepts