Moving in a circle means accelerating toward the centre, even at constant speed. That acceleration needs a resultant force, the centripetal force, supplied by tension, friction or gravity.
A body in uniform circular motion accelerates toward the centre, a = rω² = v²/r, so the resultant force is F = mrω² = mv²/r, also toward the centre.
Swing a ball on a string in a vertical circle. The string tension is the centripetal force, and it changes around the loop: largest at the bottom, smallest at the top. Energy makes the ball fastest at the bottom, which is exactly where the most force is needed.
Now a horizontal circle. The string sweeps out a cone, and it is the horizontal component of the tension that supplies the centripetal force while the vertical component balances the weight. Same physics, F = mv²/r, supplied by a real force resolved into components.
Because the velocity changes direction, a body in uniform circular motion accelerates toward the centre with a = rω² = v² / r. By Newton's second law the resultant force is also toward the centre, F = mrω² = mv² / r. This centripetal force is not a new force: it is supplied by whatever real force acts inward, friction on a turntable, tension in a string, gravity for an orbit, or the horizontal part of a contact force on a banked track.
Four quick checks on the direction of the acceleration and on F = mv²/r. Each correct answer earns XP and lights this skill on your star map.
An object moves in a circle at constant speed. The direction of its acceleration is:
The centripetal force on a body moving in a circle is best described as:
A 0.50 kg ball moves in a circle of radius 0.80 m at 4.0 m s⁻¹. The centripetal force F = mv²/r is:
Keeping the mass and radius fixed, doubling the speed changes the centripetal force to:
There is no outward "centrifugal" force on the body. The single resultant force points inward and is the centripetal force; the feeling of being thrown outward is just inertia, the body trying to travel straight while the inward force curves its path. At the top of a vertical circle the centripetal force is weight plus tension, so at the minimum speed the tension falls to zero and gravity alone provides mv²/r.
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