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Swing a bucket of water in a vertical circle over your head and at the top — bucket upside down — the water stays in. Slow down a little and you get soaked. What holds the water in, and how slow is too slow?
Swing a bucket of water in a vertical circle over your head and at the top — bucket upside down — the water stays in. Slow down a little and you get soaked. What holds the water in, and how slow is too slow?
Nothing pushes the water outward; the bucket is yanked inward faster than gravity can pull the water out, so the bottom keeps catching the falling water. Below a critical speed gravity wins — the same inward 'centripetal' force that bends every roller-coaster loop, satellite orbit, and highway curve.
An object moving in a circle is always accelerating toward the centre — even at constant speed — because its velocity DIRECTION keeps changing, and any change in velocity needs a force. This centripetal ('centre-seeking') force points inward, perpendicular to the velocity.
As the velocity vector rotates while keeping length v, its inward change Δv works out to ac = v²/r toward the centre; times mass gives Fc = mv²/r. The simulation makes this visible: double v and Fc jumps ×4, double m and it doubles, halve r and it doubles. Centripetal force is never a new force — it's SUPPLIED by something familiar: tension (ball on a string), gravity (a satellite), friction (a car on a bend), or the normal force (a loop or bucket rim). Identifying the supplier is the key to every problem. At the top of a vertical loop, gravity can supply at most mg of inward force, setting the minimum speed v_min = √(gr) for the cart — or the water — to stay in contact. **Connect it:** is not a new force law — it is what Newton's second law demands when a velocity vector changes direction at constant magnitude; some real force (tension, gravity, friction, the road) must be drafted to supply , and if none can, the circle ends and the body departs along the tangent.
Thinking a force flings you OUTWARD — the net force actually points INWARD (centripetal); you feel pushed out only because your inertia wants to go straight.