F_c = m × v² / r
Using linear velocity
F_c = m × r × ω²
Using angular velocity
Car on curved road
1000 kg car, 50 m radius, 20 m/s → 8000 N
Spinning ball on string
0.5 kg ball, 1 m string, 5 m/s → 12.5 N
Satellite orbit
Provides gravitational centripetal force
Centripetal force is the force that acts on an object moving in a circular path, directed toward the center of the circle around which the object is moving. The word "centripetal" comes from Latin, meaning "center-seeking." This force is essential for any object to maintain circular motion rather than moving in a straight line according to Newton's first law of motion.
It's important to note that centripetal force is not a fundamental force like gravity or electromagnetism. Rather, it describes the net force required to keep an object moving in a circle. This force can be provided by various sources such as tension in a string, friction between tires and road, gravitational attraction, or electromagnetic forces, depending on the physical situation.
The centripetal force formula F_c = mv²/r shows that the force depends on three factors: the mass of the object, its velocity, and the radius of the circular path. Notice that velocity is squared, which means doubling the speed quadruples the required force. This is why high-speed turns require much more force than slow turns, and why race tracks have banked curves.
The alternative formula F_c = mrω² uses angular velocity (ω) instead of linear velocity. Angular velocity measures how fast an object rotates in radians per second. The relationship between linear and angular velocity is v = ωr, which is why both formulas give identical results when properly applied. Using angular velocity is often more convenient for rotating systems like wheels, gears, and planetary motion.
Centripetal force calculations are estimates based on ideal circular motion. Actual force may vary due to friction, gravity, air resistance, or other external forces. This calculator assumes uniform circular motion with constant speed and does not account for real-world factors such as changing velocity, non-circular paths, or energy losses. For engineering applications, consult with qualified professionals and use appropriate safety factors.