Circular motion. Centripetal acceleration and force

12/03/2026

The online centripetal acceleration and force simulations on this page will allow you to know and understand much better how are the forces acting in the circular motion of an object. In particular, you will learn what centripetal acceleration and centripetal force are.

Centripetal acceleration

For a circular motion to occur it is necessary that the moving object has a centripetal acceleration, i.e. an acceleration directed towards the center of the trajectory circumference. It is this centripetal acceleration that continuously modifies the velocity and causes the circular motion. For this centripetal acceleration to exist, it is necessary the existence of a centripetal force that generates the acceleration.

Centripetal force

The centripetal force is the only one strictly necessary for the existence of a circular motion. The centripetal force can be caused, for example, by gravity, as occurs in planetary motion, or, for example, by the tension of a cable as occurs in the spinning motion of a hammer throw. The magnitude of the centripetal force is determined by the mass of the object, its velocity and the radius of the trajectory.

Other forces and accelerations of circular motion

In addition to centripetal force an object in circular motion can be affected by other forces, such as frictional forces, electromagnetic forces, etc. Understanding and analyzing these forces is essential to understand and predict the circular motion of an object in different situations.

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Centripetal acceleration and force simulations

Straight
Angle
Acceleration
Force
Station

Force on straight motion

Angle between force and velocity

This simulation allows you to change the angle between the force and velocity vectors and check how it affects the trajectory.

Centripetal acceleration

Centripetal force

Space station

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Daniel Bernoulli

1700

–

1782

Daniel Bernoulli formulated Bernoulli’s principle and developed fundamental theories in fluid mechanics and gas dynamics

“Nature is always economical in its means”

Augustin-Louis Cauchy

1789

–

1857

Augustin-Louis Cauchy formalized mathematical analysis, providing rigor to calculus and function theory, influencing mathematical physics

“Rigor in mathematics is the key to understanding physical phenomena”

Become a giant

Your path to becoming a giant of knowledge begins with these top free courses

Free mode

Mechanics, Part 2

Free mode

Mechanics, Part 1

Free mode

Dynamics and Control

Free mode

AP® Physics 2: Challenging Concepts

Free mode

AP® Physics 1 – Part 4: Exam Prep

Free mode

AP® Physics 1 – Part 1: Linear Motion

Free mode

Pre-University Physics

Professional development for Educators

Your path to becoming a giant of knowledge begins with these top free courses

Free mode

Teach kids computing: Programming

Free mode

Teach teens computing: Encryption and cryptography

Free mode

Reimagining higher education teaching in the age of AI

Free mode

Teach teens computing: Impact of technology

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Galileo Galilei

1564

–

1642

Galileo Galilei revolutionized astronomy by observing planets, Jupiter’s moons, and advocating heliocentrism.

“And yet it moves”

Gottfried Wilhelm Leibniz

1646

–

1716

Gottfried Wilhelm Leibniz was one of the founders of infinitesimal calculus, created modern mathematical notation, and contributed to mechanics and optics with groundbreaking theories

“Music is the hidden exercise of arithmetic of the soul, which does not know it is calculating.”

Become a giant

Your path to becoming a giant of knowledge begins with these top free courses

Free mode

Mechanics, Part 2

Free mode

Mechanics, Part 1

Free mode

Dynamics and Control

Free mode

AP® Physics 1 – Part 2: Rotational Motion

Free mode

AP® Physics 1: Challenging Concepts

Free mode

AP® Physics 1 – Part 4: Exam Prep

Free mode

Circuits for Beginners

Professional development for Educators

Your path to becoming a giant of knowledge begins with these top free courses

Free mode

Teach teens computing: Programming in Python

Free mode

Teach computing: Moving from Scratch to Python

Free mode

Teach kids computing: Computing systems and networks

Free mode

The Science of Learning – What Every Teacher Should Know

Test your knowledge

What role does centripetal force play in circular motion, and why is it indispensable for maintaining a curved trajectory?

Centripetal force is the net force directed toward the center of a circular path. It is not a new or special type of force; rather, it is the resultant of the real forces acting toward the center—such as tension, gravity, friction, or a combination of them. Its purpose is to continuously change the direction of the object’s velocity, keeping it on a curved path instead of moving in a straight line. Without this inward‑directed force, the object would follow a straight trajectory due to inertia. This makes centripetal force essential for understanding systems like orbiting satellites, vehicles taking a curve, rotating machinery, and any situation where an object follows a circular path.

How are speed, radius, and centripetal force related, and what does this imply for the stability of systems in circular motion?

Centripetal force increases with the square of the speed and decreases as the radius becomes larger. This means that even a small increase in speed dramatically raises the force required to maintain the circular path, while a wider curve reduces the demand. This relationship has major practical implications: a vehicle needs much more friction to take a tight curve at high speed; a rotating machine experiences rapidly increasing internal stresses as its angular speed rises; and orbital mechanics depend critically on the balance between speed and radius. Understanding this dependency is key to predicting when a system will remain stable and when it will fail to maintain circular motion.

Why do I feel like something is “pushing me outward” when a car takes a sharp turn? Does that make sense if the real force is inward?

It makes perfect sense. What you feel is not an outward force but your own inertia. Your body wants to continue moving in a straight line while the car turns underneath you. Because the seat or the door pushes you inward to force you into the curve, you perceive a pressure outward. That sensation is an inertial effect, not a physical force acting away from the center.

What happens if the centripetal force isn’t strong enough to keep the object on the circular path? How come it suddenly “flies off”?

If the available centripetal force is smaller than what the motion requires for that speed and radius, the object can no longer follow the curve. At that moment, inertia takes over and the object leaves the circular path along a straight line tangent to the curve. This explains why a car skids outward on a fast turn or why a stone tied to a string shoots off when the string breaks: the inward force becomes insufficient, so the object reverts to straight‑line motion.

How come increasing the speed just a little makes it so much harder to stay on a tight curve? Shouldn’t it only matter a bit?

It matters a lot because centripetal force depends on the square of the speed. A small increase in speed produces a disproportionately large increase in the force required to maintain the curve. In a tight curve—where the radius is already small—the demand becomes even more extreme. That’s why vehicles must slow down before entering sharp turns: the combination of high speed and small radius multiplies the required inward force beyond what friction or traction can provide.