Centripetal Force Calculator
Circular motion & force calculator
Calculation Mode
Circular Motion Parameters
Circular Motion Visualization
Motion Breakdown
Force vs Velocity
Force vs Radius
Real-World Centripetal Force Examples
Click on an example to use its values in the calculator
| Scenario | Mass | Velocity | Radius | Force |
|---|
Car Turning at Different Speeds
1000 kg car turning on a 50m radius curve at various speeds
| Speed | Velocity (m/s) | Centripetal Force | Acceleration | Safe? |
|---|
Interesting Facts
Satellites
ISS orbits at 7.66 km/s, 408 km altitude, experiencing 0.22 N/kg centripetal force
Car Turning
A car at 100 km/h on a 50m curve needs 15,432 N of force (about 1.57 g)
Roller Coasters
Loop-the-loop requires minimum velocity of √(gr) at the top
Earth's Orbit
Earth orbits Sun at 30 km/s, 150 million km radius, taking 365 days
Understanding Centripetal Force
What is Centripetal Force?
Centripetal force is the force that keeps an object moving in a circular path. It always points toward the center of the circle. The word "centripetal" means "center-seeking" in Latin.
- Direction: Always toward the center of the circle
- Perpendicular: Perpendicular to the velocity vector
- Not a new force: It's provided by other forces (gravity, tension, friction)
- Named after: Isaac Newton's work on circular motion
Key Formulas
The fundamental equations of circular motion:
- Centripetal Force: F = mv²/r
- Centripetal Acceleration: a = v²/r
- Velocity from Force: v = √(Fr/m)
- Radius from Force: r = mv²/F
- Mass from Force: m = Fr/v²
- Angular Velocity: ω = v/r
- Period: T = 2πr/v = 2π/ω
- Frequency: f = 1/T = ω/(2π)
Centripetal vs Centrifugal
Two related but different concepts:
- Centripetal Force: Real force toward center (inertial frame)
- Centrifugal Force: Apparent outward force (rotating frame)
- Example: When car turns, you feel pushed outward (centrifugal), but friction pushes you inward (centripetal)
Real-World Applications
- Orbital Mechanics: Satellites, planets, moons
- Transportation: Cars turning, trains on curves
- Amusement Parks: Roller coasters, merry-go-rounds
- Sports: Hammer throw, cycling on velodrome
- Engineering: Centrifuges, washing machines
Minimum Velocity in Vertical Circle
For an object to complete a vertical circle:
- At top: v_min = √(gr) (gravity provides centripetal force)
- At bottom: v = √(5gr) (from energy conservation)
- Tension at top: T = m(v²/r - g)
- Tension at bottom: T = m(v²/r + g)
Key Takeaways
F = mv²/r
Centripetal force is proportional to mass and v², inversely to radius
Center-Seeking
Centripetal force always points toward the center of the circle
v² Relationship
Doubling velocity quadruples the required centripetal force
Not a New Force
Centripetal force is provided by existing forces (gravity, tension, friction)
Understanding Centripetal Force
Centripetal force is a fundamental concept in physics that describes the force required to keep an object moving in a circular path. From satellites orbiting Earth to cars turning corners, centripetal force governs circular motion in our universe. Understanding these principles is essential for physics, engineering, astronomy, and many other fields.
Centripetal Force Formulas
Key formulas for circular motion calculations:
- Centripetal Force: F = mv²/r
- Centripetal Acceleration: a = v²/r
- Angular Velocity: ω = v/r
- Period: T = 2πr/v
- Frequency: f = 1/T
- Kinetic Energy: KE = ½mv²
Key Relationships
Important relationships in circular motion:
- Force ∝ v²: Doubling velocity quadruples the force
- Force ∝ m: Force is directly proportional to mass
- Force ∝ 1/r: Smaller radius requires more force
- Centripetal vs Centrifugal: Real inward force vs apparent outward force
Real-World Examples
Centripetal force in everyday life:
- Satellites: Gravity provides centripetal force for orbit
- Cars turning: Friction provides centripetal force
- Roller coasters: Normal force and gravity at loops
- Earth's orbit: Sun's gravity keeps Earth in orbit
- Washing machines: Centrifugal effect removes water
Using This Calculator
Follow these steps:
- Step 1: Select calculation mode (Force, Velocity, Radius, Mass, or Acceleration)
- Step 2: Enter the known values with appropriate units
- Step 3: Click "Calculate" to see all circular motion values
- Step 4: View circular motion visualization
- Step 5: See force vs velocity and force vs radius charts
- Step 6: Check the Examples tab for real-world cases
- Step 7: Read the Guide tab to learn circular motion theory
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