Centripetal Force Calculator
Calculate centripetal force, mass, velocity, or radius using Fc = mv²/r. Select the calculation mode below.
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What is Centripetal Force?
Centripetal force is the force required to keep an object moving in a circular path. It acts perpendicular to the direction of motion, toward the center of the circle. Without it, objects in motion follow straight-line paths. The formula is:
Fc = mv² / r
Where Fc is centripetal force in newtons (N), m is mass in kilograms (kg), v is tangential velocity in m/s, and r is the radius of curvature in meters (m). Centripetal force is essential for understanding orbits, vehicle dynamics, and rotating machinery.
Common Centripetal Force Reference Values
| Object / Event | Force (N) |
|---|---|
| Car turning a corner (1500 kg, 15 m/s, r=50m) | 6,750 |
| Earth orbiting Sun (6e24 kg, 30,000 m/s) | 35,400,000,000,000,000,000,000 |
| Roller coaster loop (500 kg, 20 m/s, r=10m) | 20,000 |
| Centrifuge (0.1 kg, 100 rad/s, r=0.2m) | 200 |
| Bicycle cornering (80 kg, 8 m/s, r=20m) | 256 |
| Satellite in orbit (1000 kg, 7500 m/s) | 5,625 |
| Washing machine spin (10 kg, r=0.3m, 1000 rpm) | 32,900 |
| Amusement ride (70 kg, r=5m, 10 m/s) | 1,400 |
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Authoritative References
Frequently Asked Questions
What is centripetal force?
Centripetal force is the force that keeps an object moving in a circular path, directed towards the center of rotation. It is defined by the formula Fc = mv²/r, where m is mass, v is tangential velocity, and r is the radius of curvature. Despite common misconception, centripetal force is not a separate force but rather any force (tension, gravity, friction) that acts toward the center.
How do I calculate centripetal force?
Centripetal force is calculated using Fc = m × v² / r. For example, a 1500 kg car turning a 50 m radius curve at 15 m/s experiences Fc = 1500 × 225 / 50 = 6,750 N of centripetal force, provided by friction between tires and road. If friction is insufficient, the car skids outward.
What is the difference between centripetal and centrifugal force?
Centripetal force is a real force directed toward the center of rotation. Centrifugal force is a fictitious (apparent) force that seems to push outward in a rotating reference frame. When you feel "pushed" against a car door during a turn, you're experiencing your inertia resisting the centripetal force of the door pushing you inward.
What happens if centripetal force is insufficient?
If the required centripetal force exceeds what is available (e.g., friction on a road, tension in a string), the object will no longer follow the circular path. It will move outward along a tangent. This explains why cars skid off curves when going too fast, and why a ball on a string flies off when the string breaks.
How does radius affect centripetal force?
Centripetal force is inversely proportional to radius: smaller radius requires more force for the same mass and speed. This is why tight turns require more friction than gentle curves, and why merry-go-rounds are more thrilling (and require more force) near the edge. Doubling the radius halves the required centripetal force.
What provides centripetal force in different situations?
Different forces provide the centripetal force depending on the situation: friction (car turning), tension (ball on string, satellite cable), gravity (orbiting satellites, planets), normal force (roller coaster loop), magnetic force (charged particles in magnetic fields), and lift (airplane banking). In each case, these forces point toward the center of the circular path.