Centripetal Force Calculator

Calculate the centripetal force required to maintain circular motion given the object mass, velocity, and radius of the circular path.

CENTRIPETAL FORCE
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Force (N)
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Acceleration (m/s²)
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Angular Vel. (rad/s)
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Period (s)
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What Is Centripetal Force?

Centripetal force is the net inward force that causes an object to follow a curved or circular path. The word "centripetal" means "center-seeking." Without this inward force, an object would continue in a straight line according to Newton's first law. Centripetal force is not a type of force itself but rather the role played by whatever force (gravity, tension, friction, etc.) provides the inward acceleration.

For a satellite orbiting Earth, gravity provides the centripetal force. For a car turning on a flat road, friction between the tires and road provides it. For a ball on a string swung in a circle, the string tension provides the centripetal force. Understanding centripetal force is fundamental to analyzing any form of circular or curved motion in physics.

Centripetal Force Formula

Fc = m × v² / r = m × ω² × r
ac = v² / r = ω² × r

Examples in Nature

SystemSource of ForceTypical RadiusTypical Speed
Earth orbiting SunGravity1.5 × 10&sup8; km30 km/s
Car on highway curveTire friction200 m30 m/s
Electron in atomElectrostatic0.053 nm2.2 × 10&sup6; m/s
Roller coaster loopNormal + gravity10 m15 m/s

Sources of Centripetal Force

  • Gravity: planets orbiting stars, moons orbiting planets, satellites orbiting Earth.
  • Friction: vehicles turning on roads, athletes running around a track.
  • Tension: objects swung on strings, amusement park rides on cables.
  • Normal force: banked road surfaces, loop-the-loop roller coasters, rotating space habitats.

Frequently Asked Questions

What happens if centripetal force is removed?

The object immediately moves in a straight line tangent to its circular path at the point of release. This is Newton's first law in action: without a net force, objects move in straight lines. This principle is used in sling weapons, hammer throw, and discus throw, where the projectile is released tangentially.

Why does centripetal force not do work?

Centripetal force is always perpendicular to the velocity (directed inward while the object moves tangentially). Since work equals force times displacement in the direction of force, and there is no displacement in the radial direction for circular motion, centripetal force does zero work. This means it changes the direction of velocity but not the speed.

How fast can a car turn without sliding?

The maximum speed for a turn is v = sqrt(μgR), where μ is the coefficient of friction (about 0.7-0.8 for dry tires on asphalt) and R is the turn radius. For a 50-meter radius turn with μ = 0.7: v = sqrt(0.7 × 9.81 × 50) = 18.5 m/s or about 67 km/h. Banked turns allow higher speeds because the normal force contributes to centripetal force.