Centripetal Force (2D) | mysimulator.uk

Whirled Ball

Mass m 1.0 kg

Radius r 1.6 m

Angular velocity ω 3.0 rad/s

Live Readout

State: circling on the string

Speed v = ωr

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Centripetal force F

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Mass

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Radius

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How it works

A ball on a string moves in a circle only because the string pulls it toward the centre at every instant. That inward pull is the centripetal force; without it, Newton's first law says the ball would keep moving in a straight line.

v = ω·r
F = m·ω²·r  (equivalently F = m·v²/r)

Cut the string and the inward force vanishes instantly. The ball does not fly radially outward — that is the "centrifugal" misconception. Instead it continues along the direction it was already moving at that instant: the tangent to the circle.

Centripetal force F Velocity v

Centripetal Force (2D)

Swing a ball on a string and it never travels toward or away from your hand — it moves in a circle because the string constantly pulls it inward, toward the centre. That inward pull is the centripetal force, F = mv²/r (equivalently F = mω²r for angular velocity ω), and it is the same force that keeps a satellite in orbit, a car gripping a curve, or a rider pinned to the wall of a spinning fairground ride. This 2D top-down companion lets you dial in the ball's mass, the radius of its circular path and its angular velocity, and watch the required centripetal force and speed update live alongside animated force and velocity vectors. Cut the string at any moment and the ball does not fly straight outward as intuition often suggests — with the inward force gone, Newton's first law takes over and the ball continues in a straight line along the tangent to the circle at the instant of release, exactly as the site's interactive 3D version of this demonstration shows.