Enter the mass, tangential velocity, and radius of the object into the calculator to determine the centripetal force.

Centripetal Force Formula

The following equation is used to calculate the Centripetal Force.

Fc = (m*V^2) / r
  • Where Fc is the centripetal force (N)
  • m is the mass of the rotating object (kg)
  • V is the tangential velocity of the object (m/s)
  • r is the radius of rotation (m)

To calculate the centripetal force, multiply the mass by the velocity squared, then divide by the radius of rotation.

What is a Centripetal Force?

Definition:

A centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the body’s motion and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as “a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a center.”

In Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits. One typical example involving centripetal force is when a body moves with constant speed along a circular path. The centripetal force is directed towards the center of the circle in which the object moves, causing uniform circular motion. The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens.

How to Calculate Centripetal Force?

Example Problem:

The following example outlines the steps and information needed to calculate Centripetal Force.

First, determine the mass of the object. For this example, the object will have a mass of 50 kg.

Next, determine the velocity of the object. In this case, the instantaneous velocity is measured as 25 m/s.

Next, determine the radius of rotation. For this problem, the radius is found to be 5 m.

Finally, calculate the centripetal force using the formula above:

Fc = (m*V^2) / r

Fc = (50*25^2) /5

Fc = 6,250 N

FAQ

What are some common examples of centripetal force in everyday life?

Centripetal force can be observed in many everyday situations. For example, when a car turns a corner, the centripetal force is what keeps it on its curved path. Similarly, when an object is tied to a string and swung in a circular motion, the tension in the string provides the centripetal force. Another common example is the force experienced by riders in a roller coaster as it navigates through loops and turns.

How does centripetal force relate to gravity?

Gravity can act as a centripetal force in certain contexts, such as in the orbits of planets and satellites. In these cases, the gravitational attraction between the orbiting body and the central body (like the Earth and the Moon, or the Sun and the planets) provides the centripetal force necessary to keep the orbiting body in its circular or elliptical path. This is a key principle in understanding astronomical orbits and the behavior of celestial bodies.

Can centripetal force be felt by an object in circular motion?

While objects in circular motion experience centripetal force, they do not “feel” this force in the way we might feel a push or pull. Instead, what is often felt is the reaction force to the centripetal force, sometimes referred to as the “centrifugal” force in a rotating reference frame. For example, when taking a sharp turn in a car, the sensation of being pushed outward is actually due to your body’s inertia and the car providing the centripetal force to change your direction, not an outward force acting on you.