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Centripetal Force Calculator

Calculate centripetal force, acceleration, and velocity for objects in circular motion with interactive visualization

Parameters

kgⓘ
Mass of the object
m/sⓘ
Tangential velocity (leave 0 to calculate from angular velocity)
mⓘ
Radius of circular path
rad/sⓘ
Angular velocity (leave 0 to calculate from period)
sⓘ
Time for one complete revolution
Circular Motion Analysis
Enter values to calculate centripetal force and motion parameters

Calculated Values

Centripetal Force:
20.0000;N20.0000;N
Centripetal Acceleration:
20.0000;m/s220.0000;m/s²
Angular Velocity:
2.0000;rad/s2.0000;rad/s
Period:
3.1400;s3.1400;s
Frequency:
0.3185;Hz0.3185;Hz

Examples

Example 1: Car in Circular Turn

A 1000kg car moving at 20 m/s in a 50m radius turn.

  • Centripetal Force: 80008000
  • Centripetal Acceleration: 88
  • Angular Velocity: 0.40.4
  • Period: 15.715.7
  • Frequency: 0.0640.064

Example 2: Satellite Orbit

A 500kg satellite orbiting at 2 rad/s with 10000m radius.

  • Centripetal Force: 2000000020000000
  • Centripetal Acceleration: 4000040000
  • Angular Velocity: 22
  • Period: 3.143.14
  • Frequency: 0.3180.318

Example 3: Merry-go-round

A 50kg child on a 3m radius merry-go-round with 5s period.

  • Centripetal Force: 237237
  • Centripetal Acceleration: 4.744.74
  • Angular Velocity: 1.261.26
  • Period: 55
  • Frequency: 0.20.2

Centripetal Force and Circular Motion

Centripetal force is the force required to keep an object moving in a circular path at constant speed. It always points toward the center of the circle and is perpendicular to the object's velocity.

The magnitude of centripetal force is given by Fc = mv²/r, where m is mass, v is tangential velocity, and r is the radius of the circular path. This force is responsible for changing the direction of motion, not the speed.

Centripetal acceleration is the acceleration toward the center of the circle: ac = v²/r. This acceleration is always perpendicular to the velocity and causes the object to change direction continuously.

Angular velocity (ω) relates to tangential velocity through v = rω. The period (T) is the time for one complete revolution: T = 2π/ω. Frequency (f) is the number of revolutions per unit time: f = 1/T.

In uniform circular motion, the speed remains constant but the velocity changes direction continuously. The centripetal force provides the necessary acceleration to maintain the circular path.

Key Concepts

  • Centripetal Force: Fc = mv²/r (force toward center)
  • Centripetal Acceleration: ac = v²/r (acceleration toward center)
  • Angular Velocity: ω = v/r (rate of angular change)
  • Period: T = 2π/ω (time for one revolution)
  • Frequency: f = 1/T (revolutions per unit time)
  • Tangential Velocity: v = rω (speed along circular path)

Real-World Applications

  • Satellite Orbits: Gravitational force as centripetal force
  • Car Turns: Friction and banking provide centripetal force
  • Amusement Park Rides: Centripetal force in circular motion
  • Atomic Physics: Electron orbits around nucleus
  • Sports: Curved ball trajectories and spinning objects

Physics Equations

Centripetal Force:
Fc=mv2rF_c = \frac{mv^2}{r}
Centripetal Acceleration:
ac=v2ra_c = \frac{v^2}{r}
Angular Velocity:
ω=vr\omega = \frac{v}{r}
Period:
T=2πωT = \frac{2\pi}{\omega}
Frequency:
f=1Tf = \frac{1}{T}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Calculate Angular Velocity

Determine the angular velocity:

Equation:

ω=2πT or ω=vr\omega = \frac{2\pi}{T} \text{ or } \omega = \frac{v}{r}

Calculation:

ω=2 rad/s\omega = 2 \text{ rad/s}

Explanation:

Angular velocity can be calculated from period or from tangential velocity and radius.

2

Step 2: Calculate Tangential Velocity

Find the tangential velocity:

Equation:

v=rωv = r\omega

Calculation:

v=10 m/sv = 10 \text{ m/s}

Explanation:

Tangential velocity is the speed along the circular path.

3

Step 3: Calculate Centripetal Acceleration

Find the centripetal acceleration:

Equation:

ac=v2ra_c = \frac{v^2}{r}

Calculation:

ac=(10.00)25=20.00 m/s2a_c = \frac{(10.00)^2}{5} = 20.00 \text{ m/s}^2

Explanation:

Centripetal acceleration is always directed toward the center.

4

Step 4: Calculate Centripetal Force

Use Newton's second law:

Equation:

Fc=macF_c = ma_c

Calculation:

Fc=1×20.00=20.00 NF_c = 1 \times 20.00 = 20.00 \text{ N}

Explanation:

Centripetal force provides the necessary acceleration for circular motion.

5

Step 5: Calculate Period and Frequency

Find the period and frequency:

Equation:

T=2πω,f=1TT = \frac{2\pi}{\omega}, \quad f = \frac{1}{T}

Calculation:

T=2π2.00=3.14 sf=13.14=0.318 HzT = \frac{2\pi}{2.00} = 3.14 \text{ s} \\ f = \frac{1}{3.14} = 0.318 \text{ Hz}

Explanation:

Period is the time for one revolution, frequency is revolutions per second.

Frequently Asked Questions (FAQ)

What is centripetal force?

Centripetal force is the force required to keep an object moving in a circular path at constant speed. It always points toward the center of the circle and is perpendicular to the object's velocity.

How do I calculate centripetal force?

Use the formula Fc = mv²/r, where m is mass, v is tangential velocity, and r is the radius of the circular path. The force is always directed toward the center of the circle.

What is the difference between centripetal and centrifugal force?

Centripetal force is the real force that keeps an object in circular motion. Centrifugal force is a fictitious force that appears in rotating reference frames and points outward.

How does radius affect centripetal force?

For a given mass and velocity, centripetal force is inversely proportional to radius. Smaller radius means larger centripetal force required to maintain the same speed.

What is angular velocity?

Angular velocity (ω) is the rate of change of angular position: ω = v/r. It measures how fast an object rotates around a center point.

How are period and frequency related?

Period (T) is the time for one complete revolution, while frequency (f) is the number of revolutions per unit time. They are inversely related: f = 1/T.

Practice MCQs

  1. Centripetal force is always directed:
  2. If velocity doubles, centripetal force:
  3. Angular velocity is related to tangential velocity by:
  4. Period and frequency are:
  5. In uniform circular motion: