Centrifugal Force Calculator

General Physics

This tool helps you calculate the centrifugal force exerted on an object moving in a circular path. You can use either linear or angular velocity for the calculation.

Practical Examples

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

Car Turning a Corner

linear

A 1500 kg car is navigating a circular curve with a radius of 50 meters at a speed of 60 km/h.

Mass: 1500 kg

Radius: 50 m

Velocity: 60 kms

Laboratory Centrifuge

angular

A test tube with a sample mass of 0.1 kg is placed in a centrifuge with a radius of 0.2 meters, spinning at 3000 RPM.

Mass: 0.1 kg

Radius: 0.2 m

Velocity: 3000 rpm

Child on a Merry-Go-Round

linear

A 40 kg child is sitting 2.5 meters from the center of a merry-go-round moving at a tangential speed of 3 m/s.

Mass: 40 kg

Radius: 2.5 m

Velocity: 3 ms

Earth's Orbit

angular

Calculating the force on a 1000 kg satellite orbiting Earth. Assume an angular velocity of approximately 0.0000727 rad/s (one revolution per day) at an orbital radius of 6,771 km from Earth's center.

Mass: 1000 kg

Radius: 6771000 m

Velocity: 0.0000727 rads

Other Titles
Understanding Centrifugal Force: A Comprehensive Guide
An in-depth look at the principles, formulas, and applications of centrifugal force in our daily lives and beyond.

What is Centrifugal Force?

  • Defining the 'Apparent' Force
  • Centrifugal vs. Centripetal Force
  • The Role of Inertia
Centrifugal force is often described as an 'apparent' or 'fictitious' force that seems to push an object away from the center of a circular path. It arises from inertia—the tendency of an object to continue moving in a straight line. When an object is forced to travel in a circle, its inertia creates the sensation of an outward pull. This calculator helps quantify that force.
Key Differences
It's crucial to distinguish it from centripetal force. Centripetal force is the real, center-seeking force (like tension in a string or gravity) that keeps an object in its circular path. Centrifugal force is the reaction force, experienced from the object's rotating frame of reference, directed outward.

Conceptual Example

  • When you're in a car that makes a sharp turn, you feel pushed against the door. That sensation is the centrifugal force.
  • A washing machine's spin cycle uses centrifugal force to separate water from clothes.

Step-by-Step Guide to Using the Calculator

  • Inputting Your Data
  • Choosing the Right Velocity Type
  • Interpreting the Results
Using our tool is straightforward. Follow these steps to get an accurate calculation:
1. Enter the object's mass and select the appropriate unit (kg, g, lb).
2. Provide the radius of the circular path and its unit (m, cm, ft, in).
3. Select your calculation type: Linear Velocity (if you know the object's speed along its path) or Angular Velocity (if you know its rate of rotation).
4. Input the velocity value and its corresponding unit.
5. Click 'Calculate' to see the results.
Result Breakdown
The calculator provides two main outputs: the Centrifugal Force in Newtons (N), which measures the outward pull, and the Centripetal Acceleration, which is the acceleration required to keep the object on its circular path.

Input Example

  • For a 10 lb ball on a 3 ft string, spinning at 5 m/s, you would input Mass: 10 lb, Radius: 3 ft, and Linear Velocity: 5 m/s.

Real-World Applications of Centrifugal Force

  • Engineering and Design
  • Amusement Parks and Recreation
  • Scientific Research
Centrifugal force is a fundamental principle with countless applications:
In Engineering
Engineers use centrifugal force to design banked curves on highways, ensuring vehicles can safely navigate turns at high speeds. It's also the working principle behind centrifugal pumps and clutches.
In Science
Laboratory centrifuges spin biological samples at high speeds to separate components based on density, such as separating red blood cells from plasma.

Application Examples

  • Designing a roller coaster loop requires precise calculation of forces to keep passengers safely in their seats.
  • Cream separators in the dairy industry use centrifugal force to isolate cream from milk.

Common Misconceptions and Correct Methods

  • Is Centrifugal Force 'Real'?
  • Confusing It with Centripetal Force
  • Ignoring the Frame of Reference
The biggest misconception is whether centrifugal force is a 'real' force. In an inertial (non-accelerating) frame of reference, it is not a true force but rather the result of inertia. However, in a non-inertial (rotating) frame of reference, it is treated as a real force to make Newton's laws work.
Centrifugal vs. Centripetal
A common mistake is using the terms interchangeably. Remember: centripetal force pulls IN, centrifugal force pushes OUT. The centripetal force is the cause of circular motion; the centrifugal effect is the result.

Clarification

  • A satellite stays in orbit because Earth's gravity provides the necessary CENTRIPETAL force. From the satellite's rotating perspective, it feels a CENTRIFUGAL force balancing gravity.
  • If the string holding a spinning ball breaks, the ball flies off in a straight line tangent to the circle, demonstrating its inertia, not an outward force.

Mathematical Derivation and Formulas

  • Formula Using Linear Velocity
  • Formula Using Angular Velocity
  • Relationship Between Velocity Types
The calculation of centrifugal force depends on whether you use linear or angular velocity.
Using Linear Velocity (v)
The most common formula is: Fc = (m * v^2) / r, where 'm' is mass, 'v' is tangential velocity, and 'r' is the radius.
Using Angular Velocity (ω)
When the rate of rotation is known, the formula is: Fc = m ω^2 r, where 'ω' is the angular velocity in radians per second.
The two velocities are related by the formula v = ω * r. This allows conversion between the two formulas, ensuring consistent results.

Formula Application

  • For a 2 kg mass moving at 5 m/s in a 1m radius circle, Fc = (2 * 5^2) / 1 = 50 N.
  • For the same mass spinning at 5 rad/s, Fc = 2 * 5^2 * 1 = 50 N.