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Centripetal Force in Circular Motion

Calculate centripetal force, centripetal acceleration, angular velocity, and period for uniform circular motion. Physics calculator for mechanics, engineering, and orbital motion problems. Supports banked curves, conical pendulums, and planetary orbits.

Centripetal Force Formula

Fs = mv²/rFormula: as = v²/r

Variables:

  • FsCentripetal Force (Newtons, N)
    Centripetal Force (Newtons, N)
  • asCentripetal Acceleration (m/s²)
    Centripetal Acceleration (m/s²)
  • mMass of the object (kg)
    Mass of the object (kg)
  • vLinear velocity (m/s)
    Linear velocity (m/s)
  • rRadius of the circular path (m)
    Radius of the circular path (m)

How to Use the Centripetal Force Calculator

This calculator helps you determine the force required to keep an object moving in a circular path.

  1. 1

    Enter Mass

    Input the mass of the object in kilograms (kg).

  2. 2

    Enter Velocity

    Input the linear velocity of the object in meters per second (m/s).

  3. 3

    Enter Radius

    Input the radius of the circular path in meters (m).

  4. 4

    Calculate

    Click the calculate button to obtain the Centripetal Force (Fs) and Centripetal Acceleration (as).

💡 Tip:

  • •Ensure all units are in the SI system (kg, m/s, m) for accurate results.

Examples

Car on a Curved Road

Problem:

A 1000kg car travels around a curve with a radius of 50m at a velocity of 20m/s.

Solution:
  1. 1.Fs = mv²/r
  2. 2.Fs = 1000 * (20)² / 50
  3. 3.Fs = 1000 * 400 / 50
Result:8000 Newtons

The road must provide at least 8000 N of frictional force to prevent the car from skidding.

Satellite in Orbit

Problem:

A satellite with a mass of 500kg orbits Earth at a velocity of 7000m/s with a radius of 7,000,000m.

Solution:
  1. 1.Fs = mv²/r
  2. 2.Fs = 500 * (7000)² / 7,000,000
  3. 3.Fs = 500 * 49,000,000 / 7,000,000
Result:3500 Newtons

The gravitational force acting on the satellite is 3500 N, acting as the centripetal force.

Frequently Asked Questions

Is centripetal force a real force?
Centripetal force is a net force requirement. It is not a new fundamental force but a label for the resultant force (like gravity, tension, or friction) that points toward the center of a circular path.
What is the difference between centripetal and centrifugal force?
Centripetal force acts toward the center of rotation. Centrifugal force is a fictitious force perceived by an observer in a rotating reference frame, appearing to push objects outward.
What happens if the centripetal force is removed?
If the centripetal force is removed, the object will stop moving in a circle and will travel in a straight line tangent to the circle at the point where the force was removed, according to Newton's First Law.
Does mass affect centripetal acceleration?
No, centripetal acceleration depends only on the velocity and the radius of the path (as = v²/r). Mass only affects the magnitude of the centripetal force (Fs = ma).
Can centripetal force change the speed of an object?
No, centripetal force only changes the direction of the object's velocity, not its speed. It acts perpendicular to the direction of motion.

Related Calculators

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Kinetic Energy Calculator

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References