Centripetal Force Calculator
Calculate the centripetal force required for circular motion by combining mass, velocity, and radius inputs, then review the methodology and FAQs.
Motion Inputs
Use SI units for consistency; the calculator updates immediately after you confirm values.
F = m × v2 ÷ r
How to Use This Calculator
Enter the object’s mass, linear velocity, and circular path radius using metric units. Click "Calculate" or edit any input to refresh the computed force. Use the reset button to start from the recommended defaults.
- Confirm the mass in kilograms (kg) for the object traveling along the circle.
- Set the tangential velocity in meters per second (m/s).
- Provide the radius of the circular path in meters (m).
- Review the centripetal force (newtons) and related quantities on the results card.
Methodology
The calculator applies the classical centripetal force formula from uniform circular motion. It uses the values provided in SI units to ensure physical correctness and then displays the force with a consistent rounding strategy for comparability.
Data Source and Methodology
All calculations rely on the well-established centripetal force relationship from mechanics textbooks. HyperPhysics documents the same derivation and serves as the authoritative reference for how mass, velocity, and radius interact.
The Formula Explained
Formula: F_c = \frac{m \cdot v^2}{r}
This ratio shows how the force grows quadratically with velocity and is inversely proportional to the radius.
Glossary of Variables
- Mass (m): The object’s mass in kilograms.
- Velocity (v): The linear (tangential) speed in meters per second.
- Radius (r): The distance from the center of rotation in meters.
- Centripetal Force (Fc): The inward force required to keep the object on its path.
How It Works: A Step-by-Step Example
For a 5 kg object traveling at 3 m/s around a 2 m radius, the formula becomes F_c = (5 kg × (3 m/s)2) / 2 m. The calculator performs the same computation, yielding 22.50 N of centripetal force.
Frequently Asked Questions (FAQ)
What is centripetal force?
Centripetal force is the inward force that keeps an object moving in a circular path.
How is centripetal force calculated?
Using the formula F_c = \frac{m \cdot v^2}{r}, where velocity is squared and divided by radius before scaling by mass.
What is the role of mass?
Mass is directly proportional to the centripetal force: doubling the mass doubles the required force.
Can centripetal force be negative?
No, centripetal force is a magnitude and remains positive because it represents the inward pull.
What are the units?
The result is presented in newtons (N), the SI unit for force.