What keeps anything moving in a circle — and what happens the instant it stops. Swing a mass on a string and watch the one force that matters: the centripetal force, always pointing to the centre, with magnitude F = m·v²/r. Set the mass, radius and speed and read the force, acceleration, angular speed and period live, with the velocity arrow (tangent) and force arrow (inward) drawn each frame. Then cut the string and see the mass fly off along the tangent — not straight outward. It all runs on your device.
You are in the Physics lab.
What the arrows, the graph and the readouts are telling you.
The red arrow is the centripetal force, drawn along the radius line and always pointing to the centre; the blue arrow is the velocity, along the tangent. They sit at a right angle to each other the whole way round. The force keeps changing the direction of the velocity without changing its size, which is exactly what "moving in a circle at constant speed" means. The radius line is labelled with r so you can see the geometry the formula uses.
The companion plot draws centripetal force against speed for your current mass and radius, and the blue dot marks where you are on it. Because v is squared the curve steepens fast: slide the speed up and the dot climbs the steep part — doubling v quadruples F. Shrinking the radius or raising the mass lifts the whole curve, since F grows as 1/r and as m. The five readouts — v, ω, Fc, ac and T — update on every frame to match.
Press Cut the string (or the Release button) and the inward force vanishes. With no net force Newton's first law takes over and the mass travels in a straight line at constant velocity — along the tangent it had at the instant of release. It does not shoot outward along the radius. Watching that tangential flyoff is the fastest cure for the most common misconception about circular motion.
One inward force, a right angle, and Newton's first law waiting in the wings.
To move in a circle at constant speed, an object must accelerate — not because its speed changes, but because its direction does. That acceleration points to the centre, a = v²/r, so by Newton's second law there must be a net inward force F = m·v²/r. It is always some real force in disguise: string tension here, gravity for a satellite, friction for a car cornering.
Because v is squared, speed dominates: going twice as fast needs four times the force. A tighter circle (smaller r) also needs more force, and a heavier mass needs proportionally more. The angular speed ω = v/r and period T = 2π/ω tell you how quickly it goes around. Slide the three controls and watch all four readouts respond.
The velocity is tangent to the circle, perpendicular to the force. Remove the force — press Release — and Newton's first law takes over: no net force means straight-line motion at constant velocity, along that tangent. It does not shoot outward along the radius. Seeing the tangential flyoff is the fastest way to fix the most common misconception about circular motion.
Teaching circular motion? You can embed this simulator on your own site free — one line of code, no sign-up.