Speed is a scalar (how fast); velocity is a vector (speed plus direction). Drag the sliders below to set an object circling at a constant speed and radius, and watch its velocity keep changing direction even as the speed holds still.

Same Speed, Never the Same Velocity

Your speedometer would look boring in this sim. Set the Speed slider to any value and watch the number sit perfectly still, minute after minute, while the object loops around the circle. Yet the velocity arrow attached to that object refuses to hold a pose: it swings, rotates, and points somewhere new at every instant. That single picture captures the whole distinction. Speed is a scalar, the plain magnitude of how fast you are going. Velocity is a vector, bundling that magnitude together with a direction.

Because the arrow always lies along the tangent to the path, its direction changes continuously as the object circles, even though its length never grows or shrinks. So a constant speed does not buy you a constant velocity. Drag the Radius slider wider and the loop stretches; one lap now covers a distance of 2·π·radius, yet the reading stays fixed while the direction keeps turning. Any change in velocity, direction included, means the object is accelerating, so it accelerates the entire time, pulled by a centripetal acceleration aimed straight at the centre.

Confuse the two words and half of rotational motion stops making sense; you would expect no acceleration whenever the speedometer holds steady, and you would be wrong. Keep the vector and the scalar separate and orbits, turns, and spinning wheels all fall into place. Pin down a single reading with the velocity calculator, then step sideways into the wider collection of motion sandboxes.

Frequently asked questions

What is the difference between speed and velocity?

Speed is a scalar — how fast, with magnitude only. Velocity is a vector — the speed together with a direction. Speed is the magnitude of the velocity.

Can something have constant speed but changing velocity?

Yes. An object moving in a circle at a steady speed has a constantly changing velocity, because the direction of its motion keeps turning even though its speed does not.

Is an object in circular motion accelerating?

Yes — even at constant speed. Its velocity changes direction continuously, and any change in velocity is acceleration; here it is a centripetal acceleration pointing toward the centre.

Which way does the velocity point in circular motion?

Along the tangent to the circle — the instantaneous direction of motion. The speed is simply the length of that velocity vector.

References & formula source

  • Halliday, Resnick & Walker — Fundamentals of Physics, Chapter 4 (Motion in Two and Three Dimensions).
  • Young & Freedman — University Physics with Modern Physics, §3.2–3.4 (Velocity and Acceleration Vectors).
  • R. Nave — HyperPhysics, Georgia State University, "Velocity and Speed" section.