Centripetal Force Calculator

Make use of this free centripetal force calculator that is specifically designed to calculate centripetal force. Also, you can determine other parameters that are related to the tangential motion of an object around a circular path by employing this calculator. Lets get ahead and discuss more about this specific motion type and how you could instantly determine it either manually or by using our centripetal acceleration calculator. Jump Down!

What Is Centripetal Force?

In physics:

“A force that acts on an object to keep it moving along a circular path is known as centripetal force.”

Centripetal Force Equation:

The centripetal force can be calculated using:

$$ F_{c} = \frac{mv^{2}}{r} $$

Where:

m = Mass of the object revolving
v = Velocity of the object
r = Radius of the circular path

This online centripetal force calculator uses the same formula to compute circular motion parameters. By rearranging the formula, you can quickly find any related quantity.

Radius of the Circle:

$$ r = \frac{mv^{2}}{F_{c}} $$

Velocity of the Object:

$$ v = \sqrt{\frac{r \cdot F_{c}}{m}} $$

Mass of the Object:

$$ m = \frac{F_{c} \cdot r}{v^{2}} $$

$$ \omega = \sqrt{\frac{F}{m \cdot r}} $$

Centripetal Acceleration:

“Centripetal acceleration represents the acceleration of an object moving along a circular path.”

It can be calculated using:

$$ a = \frac{v^{2}}{r} $$

Derivation of Centripetal Acceleration:

Newton’s second law of motion defines acceleration, which can also be calculated using our acceleration calculator. In addition, centripetal acceleration can be derived as follows:

According to Newton’s law:

$$ F = ma \hspace{0.25in} \ldots (1) $$

The centripetal force is given as:

$$ F_{c} = \frac{mv^{2}}{r} \hspace{0.25in} \ldots (2) $$

Derivation:

Comparing (1) and (2):

$$ \frac{mv^{2}}{r} = ma $$

Mass cancels out on both sides:

$$ a = \frac{v^{2}}{r} $$

Interesting fact: You can calculate any centripetal parameter instantly using our centripetal force calculator.

Centripetal Force Units:

Centripetal force is a type of force, so its units are the same as those for regular force:

In the SI system: Newtons (N)
In the Imperial system: Poundals (pdl)
Pound-force (lbf) is another unit used in English engineering
In CGS system: Dyne

You can also perform unit conversions for centripetal force using this free centripetal force calculator.

How to Find Centripetal Force?

In this section, we will go through a couple of examples to clarify the concept of circular motion and centripetal force.

Example # 01:

Calculate the centripetal force of a car moving at 5 m/s along a circular road of radius 67 m. The mass of the car is 700 kg.

Solution:

Using the centripetal force equation:

$$ F_{c} = \frac{mv^{2}}{r} $$

$$ F_{c} = \frac{700 \cdot 5^{2}}{67} $$

For velocity calculations, you can use the velocity calculator.

$$ F_{c} = \frac{700 \cdot 25}{67} $$

$$ F_{c} = \frac{17500}{67} $$

$$ F_{c} \approx 261.19 \, N $$

You can verify this result using our free online centripetal force calculator.

Example # 02:

A bike moves at 6 m/s along a circular path of radius 5 m. Find the centripetal acceleration.

Solution:

The centripetal acceleration formula is:

$$ a = \frac{v^{2}}{r} $$

$$ a = \frac{6^{2}}{5} $$

$$ a = \frac{36}{5} $$

$$ a = 7.2 \, m/s^{2} $$

How Centripetal Force Calculator Works?

Here’s how our free centripetal force calculator helps you analyze circular motion:

Input:

Select the parameter you want to calculate from the first dropdown menu
Enter the required values in the designated fields
Select the appropriate units for each value
Click the "Calculate" button

Output:

Calculates the centripetal force
Determines the mass of the object
Calculates the radius of curvature
Computes tangential speed and centripetal acceleration
Provides step-by-step calculations

FAQ’s:

What law is centripetal force?

Centripetal force is explained using Newton’s Third Law of Motion, which states:

“To every action, there is an equal but opposite reaction.”

The centripetal force is countered by the centrifugal force, which is equal in magnitude but opposite in direction. Comparing centripetal and centrifugal forces shows how different parameters affect each in calculations.

Is gravity centripetal force?

Yes, gravity can act as a centripetal force in circular motion. For example, the gravitational pull of the Sun keeps the Earth in orbit. You can calculate centripetal acceleration due to gravity using our centripetal acceleration calculator or the formula directly.

What affects centripetal force?

The main factors affecting centripetal force are the speed of the object and the radius of the circular path.

What is the importance of force?

Force is essential in physics because it can:

Set a stationary body in motion
Slow down or stop a moving body
Accelerate a moving body
Change the size, shape, or direction of a moving body

How does friction cause centripetal force?

Static friction resists outward motion and acts radially inward along the curve. This inward friction acts as the centripetal force, allowing a vehicle or object to follow a curved path.

What force causes Earth’s centripetal motion?

Earth’s centripetal motion is caused by the gravitational pull of the Sun. This force keeps the Earth moving along its orbit. You can also use our gravitational force calculator to determine the pull between planets.

What is the relationship between centripetal force and mass?

Centripetal force is directly proportional to the mass of the object. Doubling the mass doubles the force required, while increasing mass tenfold increases the force proportionally.

Why is centripetal force necessary for circular motion?

A centripetal force is required to continuously change the direction of an object’s velocity to keep it moving in a circle. Without it, the object would move straight ahead according to Newton’s First Law.

What are 3 examples of centripetal force?

Common examples of centripetal force include:

A car turning on a curved road
A ball attached to a string rotating in a circle
A satellite orbiting a planet

Conclusion:

Centripetal force is the key phenomenon that allows objects to revolve around a circular path. Our online centripetal force calculator is designed to accurately compute the force acting on an object at any moment to maintain smooth circular motion.

References:

From the source of Wikipedia: Centripetal force, Formula, Uniform circular motion, Derivation using vectors, Nonuniform circular motion, General planar motion From the source of Khan Academy: Gravitation, Mass swinging in a horizontal circle, Yo-yo in vertical circle From the source of Lumen Learning: Centripetal Force, Banked Curves, The Coriolis Force