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Centripetal Force Calculator

Calculate centripetal force calculator calculate radial inward force Fc from mass m, velocity v, and curve radius r (Fc = m * v^2 / r). Accurate physics formulas and unit conversions for engineers, students & technicians.

Calculate Centripetal Force (F_c = m · v² / r)

Enter your physical parameters below to compute verified centripetal force metrics.

Mass of object moving in circular path in kg (e.g. 1000 kg).
Tangential velocity in m/s (e.g. 20.0 m/s = 72 km/h).
Radius of circular path in meters (e.g. 50.0 m).

Calculation Results

Primary Metric Output --
Metric Breakdown 1 --
Metric Breakdown 2 --
Metric Breakdown 3 --
Metric Breakdown 4 --
Metric Breakdown 5 --
Mathematical Standard --

Calculated using verified physical methodology: Centripetal Force: F_c = \m v^2 / r = m \omega^2 r
Centripetal Acceleration: a_c = \v^2 / r

*Note: Results represent inward radial force directed toward the center of curvature.

Quick Summary

The Centripetal Force Calculator computes center-seeking radial force ($F_c = \m v^2 / r = m \omega^2 r$) required to maintain circular motion across Newtons (N), kilonewtons (kN), and lbf.

Formula Explanation

Centripetal Force: F_c = \m v^2 / r = m \omega^2 r
Centripetal Acceleration: a_c = \v^2 / r

How It Works

The Centripetal Force Calculator multiplies mass ($m$) by squared tangential velocity ($v^2$), dividing by path radius ($r$). It outputs centripetal force ($F_c$), centripetal acceleration ($a_c = v^2/r$), and experienced G-force multiplier ($g_{load} = a_c / 9.81$).

Step-by-Step Worked Example

Practical Problem: Calculate centripetal force required for a 1,000 kg car negotiating a curve of radius $r = 50.0\text{ meters}$ at $v = 20.0\text{ m/s}$ (72 km/h).

  1. Step 1: Identify Input Parameters: Mass $m = 1,000\text{ kg}$, Velocity $v = 20.0\text{ m/s}$, Radius $r = 50.0\text{ m}$.
  2. Step 2: Calculate Centripetal Acceleration ($a_c$): $a_c = \(20.0)^2 / 50.0 = \400.0 / 50.0 = 8.00\text{ m/s}^2$.
  3. Step 3: Apply Newton's 2nd Law for Radial Motion: $F_c = m \cdot a_c$.
  4. Step 4: Execute Numeric Multiplication: $F_c = 1,000\text{ kg} \times 8.00\text{ m/s}^2 = 8,000.00\text{ Newtons (N)}$.
  5. Step 5: Convert and Interpret G-Force & Imperial Outputs: Centripetal Force $F_c = 8,000.00\text{ N} = 8.00\text{ kN} = 1,798.47\text{ lbf}$. Radial Acceleration $a_c = 8.00\text{ m/s}^2$. G-Force load: $\8.00 / 9.80665 = 0.816\text{ G}$.

Real-World Calculation Examples

Scenario 1: Automobile Highway Curve

Parameters: $m = 1,000\text{ kg}$, $v = 20.0\text{ m/s}$, $r = 50.0\text{ m}$

Result: $F_c = 8,000.00\text{ N}$ (8.00 kN, 1,798 lbf). Required tire friction force.

Scenario 2: Industrial Centrifuge Separator

Parameters: $m = 0.1\text{ kg}$, $v = 50.0\text{ m/s}$, $r = 0.1\text{ m}$

Result: $F_c = 2,500.00\text{ N}$ ($a_c = 25,000\text{ m/s}^2$ / 2,549 G). Ultra-high G separation.

Scenario 3: Roller Coaster Loop-the-Loop

Parameters: $m = 500\text{ kg}$, $v = 15.0\text{ m/s}$, $r = 10.0\text{ m}$

Result: $F_c = 11,250.00\text{ N}$ (11.25 kN, 2.29 G). Track normal force.

Scenario 4: Satellite Low-Earth Orbit

Parameters: $m = 1,000\text{ kg}$, $v = 7,670.0\text{ m/s}$, $r = 6,771,000\text{ m}$

Result: $F_c = 8,688.00\text{ N}$ ($a_c = 8.69\text{ m/s}^2$). Orbital gravity tension.

Key Benefits of Using This Calculator

Tire Traction & Curve Safety

Determines minimum friction force required to prevent vehicle skid on curved roads.

G-Force Multiplier Readout

Computes experienced radial G-force multiplier ($g_{load}$) for pilot centrifuge testing.

Multi-Unit Readouts

Outputs force in Newtons, kilonewtons (kN), lbf, and kilogram-force (kgf).

100% Free & Client-Side

Executes locally in your browser with zero latency or web server transmission.

Frequently Asked Questions (FAQ)

What is centripetal force?

Centripetal force (Fc) is the net force acting on an object in circular motion, directed radially inward toward the center of curvature (Fc = m * v² / r).

What is the formula for centripetal force?

Fc = m * v² / r = m * omega² * r, where v is tangential velocity, r is radius, and omega is angular velocity.

What is centripetal vs centrifugal force?

Centripetal force is a real inward radial force observed in an inertial frame; centrifugal force is a fictitious outward apparent force experienced within a rotating non-inertial reference frame.

What provides centripetal force for a turning car?

Static friction between tires and road surface provides the required inward centripetal force (f_s = Fc = m*v²/r).

What provides centripetal force for planetary orbits?

Gravitational attraction force F_gravity = G * M * m / r² provides the centripetal force maintaining planetary orbits.

What is the SI unit of centripetal force?

The SI unit of centripetal force is the Newton (N).

How converts Newtons to lbf?

Multiply Newtons by 0.224809 to obtain pound-force (lbf) (e.g. 8,000 N = 1,798.47 lbf).

What happens if centripetal force suddenly drops to zero?

According to Newton's First Law, the object immediately flies off in a straight line tangent to the circle at speed v.

What is banked curve angle formula?

For a curve banked at angle theta with zero friction, tan(theta) = v² / (g * r).

Does centripetal force do work on a moving object?

No, because centripetal force is perpendicular to velocity at every instant (cos(90°) = 0), work W = 0 and kinetic energy remains constant.

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