Centripetal Force Calculator

N

The Formula

The centripetal force is calculated using the following formula:

Fₙ = (m × v²) / r

Where:

  • Fₙ = Centripetal force (in newtons, N)
  • m = Mass of the object (in kilograms, kg)
  • v = Tangential velocity (in meters per second, m/s)
  • r = Radius of the circular path (in meters, m)

Example Calculations

Click on any example below to load it into the calculator:

Car on a Curve

Mass: 1200 kg

Velocity: 25 m/s (90 km/h)

Radius: 50 m

Satellite Orbit

Mass: 500 kg

Velocity: 7660 m/s

Radius: 6,371,000 m (Earth radius + 200km)

Amusement Park Ride

Mass: 70 kg (person)

Velocity: 10 m/s

Radius: 5 m

Atomic Scale

Mass: 9.11×10⁻³¹ kg (electron)

Velocity: 2.2×10⁶ m/s

Radius: 5.3×10⁻¹¹ m (Bohr radius)

Applications of Centripetal Force

  • Vehicle Dynamics: Calculating the force needed to keep a car on a curved path at different speeds.
  • Amusement Park Rides: Understanding the forces acting on roller coasters and spinning rides.
  • Orbital Motion: Studying satellites orbiting planets and the centripetal force that keeps them in orbit.
  • Physics Education: Teaching students about circular motion and real-world applications of centripetal force.
  • Particle Physics: Calculating forces in particle accelerators where particles move in circular paths.
  • Astronomy: Understanding the motion of planets, stars, and galaxies under gravitational centripetal forces.

About Centripetal Force

Centripetal force is the force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.

Centripetal force is not a fundamental force but rather a description of the net force causing the circular motion. It can be provided by various forces depending on the situation:

  • Tension (in a string spinning a ball)
  • Gravity (for satellites orbiting planets)
  • Friction (for cars rounding curves)
  • Normal force (for roller coasters in loops)

The concept was first described by Christiaan Huygens and later by Isaac Newton in his laws of motion.