Centripetal Force Calculator
Compute centripetal force, required tension, or radius for circular motion using Fc = mv^2/r or Fc = mw^2/r. Ideal for students and engineers.
centripetal force calculator:
Use this Centripetal Force Calculator to instantly compute the inward force required for circular motion: enter any two of mass (m), linear speed (v) or angular speed (ω), radius (r), or force (F), and the tool solves the unknown using \( F_{c} = \frac{mv^{2}}{r} (or,F_{c} = mw^{2}r)\) Results include centripetal acceleration, unit conversions (RPM ↔ rad/s), step-by-step substitutions, and warnings when inputs imply unrealistic or unsafe conditions.
centripetal force tool Formula:
A Centripetal Force Calculator computes the inward force required to keep an object moving in a circular path. Use it to find centripetal force Fc, centripetal acceleration ac, radius r, or speed v given the other variables. The calculator supports both linear-speed and angular-speed inputs, using the equivalent formulas
\[ F_{c} = \frac{mv^{2}}{r} (or,F_{c} = mw^{2}r). \]
(where ω is angular velocity in rad/s). It’s useful for physics homework, lab analysis, mechanical design (shafts, flywheels), and vehicle dynamics (lateral load on tires). Inputs accept units like kilograms, meters, seconds, m/s, RPM (auto-converted), and newtons. Outputs show numeric answers with chosen units, step-by-step algebraic substitution for learning, and diagnostics (e.g., extremely high forces or unrealistic radii flagged). Optional features include converting RPM ↔ rad/s, solving for required mass or safe speed limits under a given force capability, and exporting results as CSV for reports.
⚡ Work & Installation Input to Output:
Input: user provides any combination of mass (m), linear speed (v) or RPM/ω, radius (r), or force (F); selects units (kg, g, m, cm, m/s, km/h, RPM, N).
Processing: Inputs are validated and converted to SI (kg, m, s, rad/s). The solver picks the appropriate formula set and algebraically isolates the unknown \( r = \frac{mv^{2}}{f_{c}}, v = \sqrt{\frac{F_{c}r}{m}}, w = \sqrt{\frac{F_{c}}{mr}} \) If RPM provided, convert to ω using ω = 2π⋅RPM/60. The tool checks edge cases (r = 0, negative mass/force) and returns physical-valid solutions only.
Output: numeric result(s) with units, step-by-step math, derived values (centripetal acceleration ac, tangential speed if ω known), diagnostic messages (e.g., “Required force exceeds material limit”), and copy/CSV export options.
Testing and Final Adjustments
Test computational exceptions: small radii (large speeds) (e.g., centrifuge examples) and cornering speeds of vehicles and as well as calculation of RPM to rad/s. Check unit conversions (km/h and m/s, RPM and rad/s), zero and negative input, and accuracy with very large/small numbers. Assure quadratic/derived-solution branches (e.g., solve v). Tests of usability: make sure that the numeric keypad is visible on mobile, labels are used to confirm direction (inward/centripetal), and non-realistic warnings (force beyond tensile strength). Introduce presets: “swinging ball, car at corner, centrifuge tube. Last OE has tooltips on the formula, ARIA Accessibility label, printable result summary and SEO Metadata to enhance discoverability.
Frequently Asked Questions - Centripetal Force Calculator:
What is centripetal force?
Centripetal force is the inward force required to keep an object moving in a circular path; mathematically F_c = m v^2 / r.
How do I compute centripetal acceleration?
Use a_c = v^2 / r or a_c = ω^2 r depending on whether you have linear or angular speed.
Can I input RPM instead of m/s?
Yes — RPM converts to angular velocity ω via ω = 2π·RPM / 60 and is used in F_c = mω^2 r.
What if I want radius from force, mass and speed?
Rearrange the formula: r = m v^2 / F_c to solve for radius.
What units should I use?
Use SI units for accuracy: kilograms (kg), meters (m), seconds (s) or provide other units — the tool auto-converts.
Does the calculator consider friction or tilt?
No — this calculates ideal centripetal force only. Effects like friction, banking angle, or air resistance are outside its scope.
Why did I get an unrealistically high force?
High force often comes from high speed and small radius (F∝v²/r). Check inputs and unit consistency; the tool flags unrealistic magnitudes.
Can I compute required tension in a string?
Yes — for an object on a string in horizontal circular motion, tension ≈ centripetal force if no other vertical forces act.
Is direction included in results?
The calculator reports magnitude of centripetal force; direction is always inward toward the circle center (normal to velocity).
Who should use this calculator?
Students, lab technicians, mechanical engineers, and anyone designing rotating systems or analyzing circular motion can use it.
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