Centripetal Force Calculator

General Physics

This tool computes the force that keeps an object in a circular path. Provide the object's mass, its velocity, and the radius of the circle to find the centripetal force.

Practical Examples

Explore real-world scenarios to understand how the calculator works.

Car Turning a Corner

Car Turning

A 1500 kg car makes a turn with a radius of 50 meters at a speed of 15 m/s. Calculate the centripetal force required to keep it on the road.

Mass: 1500 kg

Velocity: 15 m/s

Radius: 50 m

Satellite in Orbit

Satellite Orbit

A 500 kg satellite orbits the Earth at a radius of 6,800 km and a speed of 7,600 m/s. Find the centripetal force exerted by Earth's gravity.

Mass: 500 kg

Velocity: 7600 m/s

Radius: 6800 km

Child on a Merry-Go-Round

MerryGoRound

A 40 kg child sits on a merry-go-round 2 meters from the center. The ride spins at a velocity of 3 m/s. What is the centripetal force on the child?

Mass: 40 kg

Velocity: 3 m/s

Radius: 2 m

Object Swung on a String

SwingingObject

A 0.5 kg ball is swung in a horizontal circle with a 1.2-meter long string. If the ball's speed is 4 m/s, what is the tension in the string (which provides the centripetal force)?

Mass: 0.5 kg

Velocity: 4 m/s

Radius: 1.2 m

Other Titles
Understanding Centripetal Force: A Comprehensive Guide
Dive deep into the physics of circular motion and the force that makes it possible. This guide covers everything from the basic formula to complex real-world applications.

What is Centripetal Force?

  • Defining the 'Center-Seeking' Force
  • Centripetal vs. Centrifugal Force
  • The Role of Inertia in Circular Motion
Centripetal force, which means 'center-seeking' force, is the net force that acts on an object to keep it moving along a circular path. It is not a fundamental force of nature but rather the result of another force, such as gravity, tension, or friction. The direction of the centripetal force is always towards the center of the circle of motion.
Distinguishing from Centrifugal Force
A common point of confusion is the difference between centripetal and centrifugal force. Centripetal force is a real force directed towards the center of the circular path. In contrast, centrifugal force is an apparent or 'fictitious' force that seems to push an object outward from the center of rotation. It arises from inertia—the object's tendency to continue moving in a straight line.

Conceptual Examples

  • The Moon orbiting the Earth: Gravity provides the centripetal force.
  • A car turning a corner: Friction between the tires and the road provides the centripetal force.
  • Spinning a bucket of water overhead: The tension in your arm provides the centripetal force.

Step-by-Step Guide to Using the Centripetal Force Calculator

  • Inputting Your Variables
  • Selecting the Correct Units
  • Interpreting the Results
Our calculator simplifies finding the centripetal force. Follow these steps for an accurate calculation:
1. Enter the Mass (m)
Input the mass of the object undergoing circular motion. Use the dropdown menu to select the appropriate unit (kilograms, grams, or pounds).
2. Enter the Velocity (v)
Input the object's tangential velocity—its speed along the circular path. Select from units like meters per second, kilometers per hour, etc.
3. Enter the Radius (r)
Input the radius of the circle. This is the distance from the object to the center of its path. Choose from units like meters, kilometers, or feet.
4. Calculate and Analyze
Click the 'Calculate' button. The result will be displayed in multiple force units (Newtons, kilonewtons, and pound-force) for your convenience.

Real-World Applications of Centripetal Force

  • Engineering and Vehicle Design
  • Astronomy and Orbital Mechanics
  • Amusement Park Rides and Recreation
Banked Turns in Road Design
Engineers design banked curves on highways to increase the centripetal force acting on vehicles. The normal force from the road has a horizontal component that adds to friction, allowing cars to take turns at higher speeds safely.
Satellites and Planetary Orbits
The gravitational pull of a large body, like a planet or star, provides the necessary centripetal force to keep smaller objects, like satellites or other planets, in a stable orbit. Without this force, they would travel in a straight line off into space.
Centrifuges in Laboratories
A centrifuge spins samples at extremely high speeds. The centripetal force keeps the test tubes moving in a circle, while the inertia of denser particles causes them to separate from the lighter fluid, moving towards the bottom of the tube (which is the 'outward' direction).

Common Misconceptions and Correct Methods

  • Is Centripetal Force a New Force?
  • Does Centripetal Force Do Work?
  • What Happens if Centripetal Force Vanishes?
Misconception 1: It's a Standalone Force
A frequent mistake is to draw a free-body diagram and add 'centripetal force' as a separate force. This is incorrect. Centripetal force is the net result of other real forces (like tension, gravity, or friction) that are pointing towards the center.
Misconception 2: It Performs Work
In uniform circular motion, the centripetal force is always perpendicular to the direction of the object's displacement (which is tangential). Since work is calculated as force multiplied by displacement in the direction of the force (W = Fd cos(θ)), and the angle θ is 90 degrees, the work done by the centripetal force is zero. It changes the direction of velocity but not its magnitude (speed).
Misconception 3: An Outward Force Takes Over
If the centripetal force suddenly disappears (e.g., a string breaks), the object does not fly radially outward. Due to inertia, it continues in a straight line tangent to the point on the circle where the force was lost, as stated by Newton's First Law of Motion.

Mathematical Derivation and Examples

  • The Core Formula: Fc = mv²/r
  • Derivation from Angular Velocity
  • Worked-Out Numerical Examples
The Fundamental Formula
The most common formula for centripetal force (Fc) is given by: Fc = m * v² / r, where: 'm' is the mass of the object, 'v' is its tangential velocity, and 'r' is the radius of the circular path.
Formula with Angular Velocity (ω)
Tangential velocity (v) is related to angular velocity (ω) by the equation v = ωr. Substituting this into the main formula gives an alternative form: Fc = m * (ωr)² / r = mω²r. This version is useful when the rate of rotation is known in terms of radians per second.

Calculation Example

  • Problem: A 2 kg stone is tied to a rope of length 1.5 m and is swung in a circle at a velocity of 5 m/s. What is the centripetal force?
  • Solution: Using Fc = mv²/r, we get Fc = (2 kg * (5 m/s)²) / 1.5 m = (2 * 25) / 1.5 = 50 / 1.5 ≈ 33.33 N.