Last Updated: September 21, 2026
Centripetal vs centrifugal force is a fundamental concept in circular motion. Centripetal force acts toward the center of a circular path and keeps an object moving in that path, while centrifugal force is an apparent outward force used when motion is described from a rotating reference frame.
Who Is This Article For?
This guide is designed for high school and college physics students, teachers, and anyone learning circular motion. It helps explain the difference between centripetal and centrifugal force, understand their formulas, solve circular-motion problems, and recognize these forces in real-world examples such as turning cars, satellites, rotating rides, and objects moving on strings.
Quick AI Overview:
Centripetal force is the net real force directed toward the centre of a circular path, while centrifugal force is an apparent or fictitious force used when motion is described from a rotating reference frame. Centripetal force is required for circular motion and is calculated as F₍c₎ = mv²/r. Depending on the situation, it can be provided by friction, tension, gravity, a normal force, or another real force. The apparent outward feeling associated with centrifugal force comes from inertia and the body’s tendency to continue moving in a straight line.
Key Takeaway: Centripetal force points toward the center of circular motion and is produced by a real physical interaction. Centrifugal force appears outward only when motion is described from a rotating frame.
This guide is designed for high school and college physics students, teachers, and anyone learning circular motion. It helps explain the difference between centripetal and centrifugal force, understand their formulas, solve circular-motion problems, and recognize these forces in real-world examples such as turning cars, satellites, rotating rides, and objects moving on strings.
What Is the Difference Between Centripetal and Centrifugal Force?
The simplest way to understand centripetal vs centrifugal force is to look at their direction and reference frame.
Centripetal force acts toward the centre of a circular path. It is the net inward force required to continuously change an object’s direction of motion.
Centrifugal force, in the usual introductory-physics treatment, is an apparent or fictitious outward force that appears when motion is described from a rotating, non-inertial reference frame.
Quick Answer
Centripetal force pulls or acts inward toward the centre, whereas centrifugal force appears outward in a rotating reference frame. In an inertial reference frame, the circular motion is explained by real inward forces rather than an outward centrifugal force.
For example, when a car turns left, friction between the tyres and road provides the inward force needed to curve the car’s path. A passenger may feel as if they are being pushed toward the outside of the turn. That outward sensation is associated with inertia and can be represented as centrifugal force when using the car’s rotating frame.
Centripetal vs Centrifugal Force: Side-by-Side Comparison
| Property | Centripetal Force | Centrifugal Force |
|---|---|---|
| Direction | Toward the centre | Away from the centre |
| Role | Keeps an object moving in a circular path | Represents an apparent outward effect in a rotating frame |
| Reference frame | Can be analysed in an inertial frame | Appears when using a rotating/non-inertial frame |
| Nature | Net real force required for circular motion | Fictitious/apparent force in the rotating-frame description |
| Formula magnitude | F₍c₎ = mv²/r | Depends on the rotating-frame formulation |
| Source | Friction, tension, gravity, normal force, etc. | No physical object is required to exert it |
| Example | Tyre-road friction turning a car inward | Passenger’s apparent outward sensation in a turn |
Quick Answer
The key difference is direction and reference frame: centripetal force is the inward net force responsible for circular motion, while centrifugal force is an outward apparent force introduced when analysing motion from a rotating frame.
What Is Centripetal Force?
Centripetal force is the net force directed toward the centre of a circular path.
The word “centripetal” means centre-seeking. Whenever an object follows a circular path, its velocity continuously changes direction. Because acceleration means a change in velocity, the object is accelerating even when its speed remains constant.
That inward acceleration is called centripetal acceleration.
The relationship between centripetal acceleration and centripetal force is:
a₍c₎ = v²/r
and therefore:
F₍c₎ = ma₍c₎ = mv²/r
where:
- F₍c₎ = centripetal force in newtons
- m = mass in kilograms
- v = speed in metres per second
- r = radius of the circular path in metres
Quick Answer
Centripetal force is the net inward force that keeps an object moving in a circular path. Its magnitude is F₍c₎ = mv²/r.
Why Does Circular Motion Require a Force?
An object naturally tends to continue moving in a straight line at constant velocity unless a net external force changes its motion.
In circular motion, the object’s direction is constantly changing. Even if its speed stays exactly the same, its velocity does not remain constant because velocity includes direction.
Therefore, a net force must continually change the direction of the velocity.
That force points toward the centre of the circle.
Quick Answer
Circular motion requires a net inward force because the object’s velocity is continuously changing direction. This inward acceleration is called centripetal acceleration.
Centripetal Acceleration: Formula and Meaning
Centripetal acceleration is the inward acceleration associated with circular motion:
a₍c₎ = v²/r
It can also be written using angular velocity:
a₍c₎ = ω²r
where ω is angular velocity in radians per second.
The two forms are connected by:
v = ωr
Therefore:
v²/r = ω²r
Quick Answer
Centripetal acceleration is directed toward the centre of the circular path and can be calculated using a₍c₎ = v²/r or a₍c₎ = ω²r.
What Provides the Centripetal Force?
One of the most important concepts in circular motion is that centripetal force is not a separate fundamental type of force.
Instead, the phrase “centripetal force” describes the net inward force produced by one or more ordinary physical forces.
Depending on the situation, the centripetal force may be provided by:
- Friction — a car turning on a flat road
- Tension — a ball moving on a string
- Gravity — a satellite orbiting Earth
- Normal force — an object moving around a curved track
- A component of normal force — a banked road
- Magnetic force — a charged particle moving through a magnetic field
Quick Answer
Centripetal force can be provided by friction, tension, gravity, normal force, magnetic force, or the resultant of several real forces. “Centripetal” describes the role and direction of the force rather than a separate force type.
What Is Centrifugal Force?
Centrifugal force is commonly described as an apparent outward force associated with rotating reference frames.
Imagine sitting inside a car while it turns sharply. You may feel as though your body is being pushed toward the outside of the turn.
From the perspective of someone standing on the ground, however, your body is trying to continue along its original straight-line path while the car changes direction underneath you. The car’s seat, door, or other contact force changes your motion and provides the required inward acceleration.
When the motion is analysed from the rotating frame of the car, an outward inertial force can be introduced to make Newton’s laws usable in that non-inertial frame.
Quick Answer
Centrifugal force is an apparent or fictitious force used in a rotating reference frame to represent the outward inertial effect associated with circular motion.
Is Centrifugal Force Real?
The answer depends on the reference frame being used.
In an inertial reference frame, such as an approximately stationary frame attached to the Earth for many everyday problems, the circular motion is explained using real forces acting toward the centre. There is no additional outward force that needs to be added.
In a rotating reference frame, centrifugal force can be introduced as an inertial or fictitious force. It is mathematically useful because the observer is accelerating along with the rotating system.
This distinction is important because the word “real” can become misleading if reference frames are not specified. Physics allows different reference frames, but the equations must account correctly for whether the frame is inertial or accelerating.
Quick Answer
Centrifugal force is not a real interaction force like gravity, friction, or tension. It is an inertial/fictitious force introduced when analysing motion from a rotating reference frame.
Why Do You Feel Pushed Outward in a Turning Car?
Suppose a car turns left.
Before the turn, your body is moving approximately straight ahead. When the car changes direction, the seat and other parts of the car must exert an inward force on you so that your velocity changes with the vehicle.
Your body resists this change in motion because of inertia.
Relative to the turning car, you appear to move toward the outside of the turn.
This is why passengers often describe the experience as being “pushed outward.”
Quick Answer
You feel pushed outward in a turning car because your body tends to maintain its original straight-line motion while the car accelerates inward around the curve.
Centripetal vs Centrifugal Force Examples
Real-world examples make the distinction much easier to understand.
| Situation | Centripetal Effect | Apparent Centrifugal Effect |
|---|---|---|
| Car turning | Tyre-road friction acts inward | Passenger feels pushed outward |
| Ball on a string | Tension acts toward the centre | Ball appears to pull outward on the string |
| Washing machine | Drum provides inward contact force | Water appears to move outward |
| Satellite orbit | Gravity provides inward force | No separate outward force is needed in an inertial frame |
| Roller coaster | Track and gravity provide the required inward net force | Rider may experience an outward sensation |
| Spinning ride | Wall provides inward normal force | Rider feels pressed against the outer wall |
Quick Answer
In everyday circular-motion examples, the inward centripetal effect comes from an identifiable physical interaction, while the outward centrifugal effect describes what an observer in a rotating system may appear to experience.
Example 1: Car Turning on a Flat Road
Consider a 1,200 kg car travelling at 15 m/s around a circular bend with a radius of 50 m.
The required centripetal force is:
F₍c₎ = mv²/r
F₍c₎ = 1,200 × 15² / 50
F₍c₎ = 5,400 N
On a flat road, static friction between the tyres and road can provide this inward force.
If the available friction is less than the required centripetal force, the car cannot follow the intended circular path and may skid.
Quick Answer
For a 1,200 kg car travelling at 15 m/s around a 50 m radius bend, the required centripetal force is 5,400 N, provided by tyre-road friction on a flat road.
Example 2: Ball Moving on a String
Suppose a 0.5 kg ball moves in a horizontal circle of radius 0.8 m at 4 m/s.
Centripetal acceleration:
a₍c₎ = v²/r
a₍c₎ = 4²/0.8 = 20 m/s²
Centripetal force:
F₍c₎ = ma₍c₎
F₍c₎ = 0.5 × 20 = 10 N
If the string supplies the only horizontal force, its tension provides the 10 N centripetal force.
If the string suddenly breaks, the ball does not fly directly radially outward. It continues approximately along the tangent to the circular path at the instant of release.
Quick Answer
The string’s tension provides the centripetal force. If the string breaks, the ball moves along a tangent rather than directly outward from the centre.
Example 3: Satellite Orbiting Earth
A satellite in a circular orbit continuously accelerates toward Earth.
Gravity provides the required centripetal force:
F₍gravity₎ = F₍centripetal₎
Therefore:
GMm/r² = mv²/r
The satellite mass cancels:
v = √(GM/r)
This means that, for an ideal circular orbit around a given central body, orbital speed depends on orbital radius rather than the satellite’s mass.
Quick Answer
Gravity provides the centripetal force that keeps a satellite in circular orbit. For a circular orbit, v = √(GM/r).
Example 4: Washing Machine Spin Cycle
During a spin cycle, clothes and water move around the rotating drum.
The drum exerts contact forces on the contents, continually changing their direction of motion.
The water may appear to move outward relative to the rotating drum, which is why the holes in the drum allow water to escape.
Quick Answer
In a washing machine, the rotating drum provides the inward force needed to curve the motion of the clothes and water, while the apparent outward movement is associated with inertia and the rotating-frame description.
Centripetal Force Formula
The main centripetal force equation is:
F₍c₎ = mv²/r
Using angular velocity:
F₍c₎ = mω²r
These equations show several important relationships.
If mass increases while speed and radius remain constant, the required centripetal force increases.
If speed doubles, the required centripetal force becomes four times larger because force depends on v².
If radius increases while mass and speed remain constant, the required centripetal force decreases.
Quick Answer
The centripetal force formula is F₍c₎ = mv²/r. Because velocity is squared, doubling speed requires four times the centripetal force for the same mass and radius.
Angular Velocity and Circular Motion
Angular velocity describes how quickly an object sweeps through an angle.
For uniform circular motion:
ω = 2π/T
and:
ω = 2πf
where:
- T = period
- f = frequency
Since:
v = ωr
we obtain:
F₍c₎ = mω²r
This form is especially useful when a problem gives the period, frequency, or angular velocity rather than linear speed.
Quick Answer
Angular velocity connects circular speed with the period and frequency through ω = 2π/T = 2πf, and centripetal force can then be written as F₍c₎ = mω²r.
Centripetal Force on a Banked Road
Banked roads are designed so that part of the normal force points toward the centre of the curve.
For an ideal banked curve where friction is not required at the design speed:
N sinθ = mv²/r
and:
N cosθ = mg
Dividing these equations gives:
tanθ = v²/(rg)
Therefore:
θ = tan⁻¹(v²/rg)
Banking allows the road geometry to contribute directly to the centripetal force required for circular motion.
Quick Answer
On an ideal banked road, the inward component of the normal force provides the centripetal force, and the banking angle satisfies tanθ = v²/(rg).
Centripetal Force in Vertical Circular Motion
Vertical circular motion is more complicated because gravity changes its relationship with the inward direction as the object moves around the circle.
At the top of a loop, gravity points toward the centre.
For an object attached to a string:
T + mg = mv²/r
At the minimum speed needed to keep the string taut, tension becomes zero:
mg = mv²/r
so:
v₍min₎ = √(gr)
At the bottom of the circle, the inward direction is upward, while gravity acts downward:
T − mg = mv²/r
Therefore, the tension must provide enough inward net force after accounting for gravity.
Quick Answer
In a vertical circle, the forces contributing to centripetal force change with position. At the top, gravity may contribute toward the centre; at the bottom, gravity acts opposite to the inward direction.
What Happens If Centripetal Force Is Removed?
If the net inward force suddenly disappears, the object no longer has the acceleration required to follow the circular path.
It therefore continues in the direction of its instantaneous velocity.
That direction is tangent to the circle.
For example, if a string holding a rotating ball breaks, the ball moves along the tangent rather than travelling directly away from the centre.
Quick Answer
When centripetal force is removed, the object follows a straight-line path tangent to the circle at the point where the force disappeared.
Common Mistakes When Comparing Centripetal and Centrifugal Force
Mistake 1: Treating Centripetal Force as a New Fundamental Force
Centripetal force is not another fundamental interaction alongside gravity or electromagnetic force.
It is the name given to the net inward force responsible for circular acceleration.
Quick Answer
Centripetal force is a role played by real forces; it is not a separate fundamental force.
Mistake 2: Drawing Centrifugal Force on Every Free-Body Diagram
In an inertial-frame analysis, adding an outward centrifugal force to a free-body diagram can incorrectly double-count the physics.
The appropriate forces should be identified according to the chosen reference frame.
Quick Answer
Do not automatically add centrifugal force to an inertial-frame free-body diagram. First identify the reference frame and the actual physical forces acting on the object.
Mistake 3: Thinking an Object Flies Radially Outward When the String Breaks
When circular motion stops, the object does not instantly move radially outward.
It moves in the direction of its instantaneous velocity, which is tangent to the circle.
Quick Answer
A released object moves tangentially, not radially outward, because its instantaneous velocity is tangent to the circular path.
Mistake 4: Forgetting That Constant Speed Can Still Mean Acceleration
Acceleration is a change in velocity, and velocity includes direction.
Therefore, an object can have constant speed while still having acceleration.
Quick Answer
Uniform circular motion has constant speed but non-zero acceleration because the direction of velocity continually changes.
Centripetal Force in Everyday Life
Centripetal force appears in many ordinary situations.
When a car goes around a roundabout, friction helps provide the inward force.
When a satellite orbits Earth, gravity provides the inward force.
When a ball is swung around on a string, tension provides the inward force.
When an aircraft turns, the appropriate component of aerodynamic lift contributes to the inward acceleration.
When a roller coaster travels around a loop, gravity and track forces combine to produce the required centripetal force.
Quick Answer
Centripetal force is involved whenever an object follows a curved path, including cars turning, satellites orbiting, balls on strings, aircraft turns, and roller-coaster loops.
Centripetal vs Centrifugal Force: The Key Concept
The most useful mental model is this:
Centripetal = inward requirement for curved motion.
Centrifugal = apparent outward inertial effect in a rotating frame.
If you are analysing the motion from an approximately inertial frame, identify the real forces and determine their inward resultant.
If you are analysing the situation from a rotating frame, inertial forces such as centrifugal force can be introduced so that the equations properly describe what the rotating observer sees.
The two descriptions are not necessarily competing explanations. They are descriptions associated with different reference frames.
Quick Answer
Centripetal and centrifugal force are best distinguished by direction and reference frame: centripetal force is the inward net force required for circular motion, while centrifugal force is an outward inertial force used in a rotating-frame description.
Frequently Asked Questions
What is centripetal force?
Centripetal force is the net inward force that keeps an object moving along a circular path. Its magnitude is F₍c₎ = mv²/r.
What is centrifugal force?
Centrifugal force is an apparent or fictitious outward force introduced when motion is analysed from a rotating reference frame.
What is the difference between centripetal and centrifugal force?
Centripetal force acts toward the centre of circular motion, while centrifugal force represents an apparent outward inertial effect in a rotating frame.
Is centrifugal force real?
Centrifugal force is not a real interaction force in the same sense as gravity, tension, friction, or the normal force. It is an inertial/fictitious force used in non-inertial rotating frames.
Is centripetal force a real force?
The inward net force responsible for circular acceleration is real, but “centripetal force” is not a separate type of interaction. It may be supplied by friction, tension, gravity, normal force, or another real force.
What provides centripetal force for a car?
On a flat road, static friction between the tyres and road generally provides the required centripetal force. On a banked road, the normal force can provide some or all of the required inward force.
What provides centripetal force for a satellite?
Gravity provides the centripetal force for a satellite in a circular orbit around Earth.
What happens when centripetal force is removed?
The object stops following the circular path and moves approximately in a straight line tangent to the circle at the point where the inward force is removed.
Why does a passenger feel pushed outward in a turning car?
The passenger’s body tends to maintain its original direction of motion while the car turns inward. Relative to the car, this produces the sensation of being pushed toward the outside.
What is the centripetal force formula?
The standard formula is:
F₍c₎ = mv²/r
It can also be expressed as:
F₍c₎ = mω²r
What is the centripetal acceleration formula?
Centripetal acceleration is:
a₍c₎ = v²/r = ω²r
and it is always directed toward the centre of the circular path.
What are examples of centripetal force?
Examples include tyre-road friction on a turning car, string tension on a rotating ball, gravity acting on an orbiting satellite, and normal force acting on an object moving around a curved track.
What are examples of centrifugal effects?
Passengers feeling pushed outward in a turning vehicle, water appearing to move outward in a spinning washing machine, and riders feeling pressed against the outside wall of a rotating ride are common examples.
What is the difference between centripetal acceleration and centripetal force?
Centripetal acceleration describes the inward change in velocity, while centripetal force is the net force that produces that acceleration. They are related by F₍c₎ = ma₍c₎.
Why does an object move tangentially when released from circular motion?
At the instant it is released, its velocity is tangent to the circular path. Without the inward force needed to keep curving that velocity, it continues in a straight-line direction.
Can centrifugal and centripetal force exist together?
They can both appear in an analysis when a rotating reference frame is used. In that description, centrifugal force is an inertial force directed outward while real forces may provide the inward centripetal acceleration. The exact force accounting depends on the reference frame.
Does centripetal force always point toward the centre?
For ideal circular motion, the required centripetal acceleration and corresponding net inward force point toward the centre of curvature.
What happens to centripetal force if speed doubles?
Because F₍c₎ = mv²/r, doubling speed makes the required centripetal force four times larger when mass and radius remain unchanged.
What happens to centripetal force if the radius doubles?
If mass and speed remain constant, doubling the radius cuts the required centripetal force in half because force is inversely proportional to radius.
Final Takeaway
The distinction between centripetal vs centrifugal force becomes much easier once the reference frame and direction are clear.
Centripetal force is the net inward force required for circular motion. Centrifugal force is an apparent outward inertial force used when describing motion from a rotating reference frame.
The most important equation is:
F₍c₎ = mv²/r
But the most important conceptual point is that centripetal force is not a new kind of force. Gravity, friction, tension, normal force, magnetic force, or a combination of real forces can provide the inward net force.
Whenever an object moves in a circle, ask two questions:
- What real force or combination of forces is providing the inward net force?
- Which reference frame am I using to describe the motion?
Once those two questions are answered, the difference between centripetal and centrifugal force becomes much clearer.
Related Physics Topics
For deeper study, readers can continue with related topics such as:
- Circular motion and centripetal force
- Newton’s laws of motion
- Universal gravitation and orbital motion
- Magnetic force and circular motion
- Vectors and scalar quantities
- Work and energy in mechanics