Circular motion. Centripetal acceleration and force

09/05/2026

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.

This Thematic Unit is part of our Physics collection

Centrifugal Force

Apparent force that tends to move a body away from the center of rotation when observed from an accelerated system.

Centripetal Acceleration

Quantity that measures the change in velocity direction of a body following a curved path.

Centripetal Force

Net force directed toward the center of the trajectory that forces a body to follow a curve.

Tangent

Trigonometric ratio defined as the quotient between the opposite side and the adjacent side to an angle.

Tension

Force exerted by a rope or cable that acts as the physical cause of centripetal acceleration.

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.

Centrifugal Force

Apparent force that tends to move a body away from the center of rotation when observed from an accelerated system.

Centripetal Acceleration

Quantity that measures the change in velocity direction of a body following a curved path.

Centripetal Force

Net force directed toward the center of the trajectory that forces a body to follow a curve.

Tangent

Trigonometric ratio defined as the quotient between the opposite side and the adjacent side to an angle.

Tension

Force exerted by a rope or cable that acts as the physical cause of centripetal acceleration.

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Centripetal acceleration and force simulations

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

Johannes Kepler

1571

–

1630

Kepler formulated the three laws of planetary motion, establishing elliptical orbits and the relationship between planetary period and distance from the Sun

“The heavens teach the geometry that nature follows”

William Rowan Hamilton

1805

–

1865

William Rowan Hamilton developed Hamiltonian mechanics and quaternions, unifying geometry and mathematical physics

“Mathematics and physics meet in the harmony of the equations governing motion.”

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Joseph-Louis Lagrange

1736

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1813

Joseph-Louis Lagrange formulated the Lagrangian equations, key in classical mechanics to describe motion. He also founded variational calculus, applying it to algebra and mathematical physics

“As soon as a mathematical truth is established, it always serves as a starting point for new truth”

Archimedes

287 a.C.

–

212 a.C.

Archimedes established fundamental principles of mechanics and hydrostatics, including the famous Archimedes’ principle of buoyancy in fluids

“Give me a place to stand, and I will move the world”

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STEM Outside

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.