Centripetal force is the resultant force directed toward the centre of a circular path. It produces the inward acceleration that continually changes an object's direction of motion. It is not a separate type of force: tension, gravity, friction, the normal force, or a combination of forces can provide the required inward resultant.
This distinction is central to IB Physics circular motion. Students often remember F = mv²/r but lose marks by adding a fictional centripetal-force arrow to a free-body diagram or by confusing centripetal force with centrifugal force. This centripetal force explained guide develops the concept, equations, force diagrams, examples, and exam method without duplicating the wider treatment in IB Physics Circular Motion and Gravitation Explained.
What is centripetal force in physics?
An object moving at constant velocity would follow a straight line because of Newton's first law. To make it follow a circle, its velocity must continually turn. Since changing velocity means accelerating, circular motion requires an acceleration directed toward the centre of the circle.
Newton's second law connects that acceleration to a resultant force:
F_resultant = ma
For uniform circular motion, the radial acceleration is the centripetal acceleration:
a_c = v²/r
Therefore, the required inward resultant is:
F_c = ma_c = mv²/r
The word centripetal means centre-seeking. The label describes the direction and function of the resultant force, rather than identifying a new physical interaction.
For example, consider a ball attached to a string and moving in a horizontal circle. The string's tension, or an inward component of that tension depending on the arrangement, provides the centripetal force. It would be incorrect to draw both tension and an additional centripetal force as separate forces acting on the ball.
Why is there acceleration when speed is constant?
Speed is a scalar, but velocity is a vector with both magnitude and direction. In uniform circular motion, the speed stays constant while the direction of velocity changes at every point. The object is therefore accelerating even though it is not speeding up or slowing down.
At any instant:
- The velocity is tangent to the circular path.
- The centripetal acceleration points radially inward.
- The resultant centripetal force points radially inward.
- Velocity and centripetal force are perpendicular.
Imagine removing the inward force suddenly. The object would not continue curving outward. It would move along a straight line tangent to the circle at the point of release, as demonstrated in NASA's centripetal force classroom resource.
This is a useful way to correct a common misconception. The object does not have a natural tendency to move outward; its inertia gives it a tendency to continue with its current instantaneous velocity, which is tangential.
Centripetal force equations for IB Physics
The current IB Physics course places circular motion within A.2 Forces and momentum, which is studied by both SL and HL students. The course was first assessed in 2025, as confirmed by the official IB Physics subject brief.
The core relationships are:
| Relationship | Form | Use when given |
|---|---|---|
| Centripetal acceleration | a_c = v²/r | Linear speed and radius |
| Angular form | a_c = ω²r | Angular speed and radius |
| Period form | a_c = 4π²r/T² | Period and radius |
| Centripetal force | F_c = mv²/r | Mass, speed, and radius |
| Angular force form | F_c = mω²r | Mass, angular speed, and radius |
| Period force form | F_c = 4π²mr/T² | Mass, period, and radius |
| Linear and angular speed | v = ωr = 2πr/T | Converting between motion variables |
Here, m is mass in kilograms, v is linear speed in metres per second, r is the radius in metres, ω is angular speed in radians per second, and T is the period in seconds. Force is measured in newtons.
These equations should not be treated as disconnected formulas. They all follow from Newton's second law and the geometry of circular motion. RevisionDojo's A.2.4 Circular Motion notes provide the broader set of syllabus relationships when you need to revise the complete subtopic.
Understanding the proportionalities
From F_c = mv²/r:
- Doubling the mass doubles the required force, if speed and radius remain constant.
- Doubling the speed multiplies the required force by four, if mass and radius remain constant.
- Doubling the radius halves the required force, if mass and speed remain constant.
The stated conditions matter. If angular speed is held constant instead of linear speed, F_c = mω²r shows that force increases with radius. Always identify which quantities are fixed before describing a proportional relationship.
Which real forces provide centripetal force?
The physical source of the inward resultant depends on the situation. More than one real force can contribute, and a force does not have to point entirely inward to have a radial component.
| Situation | Real force or resultant providing the inward force |
|---|---|
| Satellite in a circular orbit | Gravitational force |
| Car turning on a level road | Static friction exerted by the road |
| Ball on a string in a horizontal circle | Tension or its horizontal component |
| Roller-coaster car in a loop | Resultant of normal force and weight |
| Charged particle in a magnetic field | Magnetic force, when perpendicular to velocity |
| Car on an ideally banked road | Horizontal component of the normal force |
The safest general equation is not simply F_c = mv²/r, but:
ΣF_inward = mv²/r
This notation reminds you to identify and combine the real forces. If outward is chosen as positive instead, the signs must change consistently.
Example: car turning on a level road
A 1200 kg car travels around a level curve of radius 50 m at 10 m s⁻¹. The required inward force is:
F_c = mv²/r
F_c = (1200)(10²)/50 = 2400 N
On a level road, static friction from the road provides this 2400 N inward force. The car is not necessarily sliding, so describing the force automatically as kinetic friction would be incorrect.
If the speed doubled to 20 m s⁻¹, the required force would become 9600 N, four times larger. This squared dependence helps explain why entering a bend too quickly substantially increases the risk of losing traction.
Example: satellite in circular orbit
For a satellite of mass m orbiting a planet of mass M, gravity provides the centripetal force:
GMm/r² = mv²/r
After cancelling m and rearranging:
v = √(GM/r)
The satellite's own mass cancels, so the circular orbital speed at a particular radius does not depend on the satellite's mass. Here, r is measured from the planet's centre, not from its surface. This radius choice is a frequent source of examination errors.
Centripetal force versus centrifugal force
Centripetal and centrifugal force are not two equal forces acting on the same object in an ordinary inertial-frame analysis. Their meanings depend on the chosen reference frame.
| Feature | Centripetal force | Centrifugal force |
|---|---|---|
| Direction | Toward the centre | Away from the centre |
| Status in an inertial frame | Inward resultant of real forces | Not a real interaction acting on the object |
| Role | Produces inward acceleration | Introduced as an inertial or fictitious force in a rotating frame |
| Free-body diagram in a ground frame | Show the real forces whose resultant is inward | Do not add it |
Suppose you are sitting in a car turning left. The seat or door pushes you left so that your body follows the car's curved path. Relative to the ground, this inward contact force accelerates you left; there is no real outward force pushing you right.
You nevertheless feel as though you are being thrown outward because your body tends to continue along its previous tangential path while the car turns underneath you. In the rotating frame of the car, physicists may introduce an outward centrifugal force so that Newtonian force equations can be applied within that non-inertial frame. OpenStax's treatment of centripetal force and rotating frames explains this frame-dependent distinction.
For most IB circular-motion questions, work in the ground or laboratory frame unless the question explicitly specifies otherwise. Draw only real interactions, then set their inward resultant equal to mv²/r.
How to draw a correct free-body diagram
A free-body diagram should show forces acting on the chosen object. It should not include velocity, acceleration, the path of motion, or mv²/r as though these were additional forces.
Use this sequence:
- Isolate the object.
- Mark the direction toward the centre separately.
- Draw all real forces, such as weight, normal force, tension, friction, or gravity.
- Resolve forces into radial and tangential components if necessary.
- Set the radial resultant equal to
mv²/r.
Consider a rider at the bottom of a vertical circular loop. The normal force N acts upward toward the centre, while weight mg acts downward away from the centre. The radial equation is therefore:
N - mg = mv²/r
It is wrong to write N = mv²/r, because weight also contributes to the radial resultant. It is equally wrong to draw a third force labelled centripetal force.
At the top of the loop, both weight and the normal force may point toward the centre, giving:
N + mg = mv²/r
The expression for the centripetal requirement remains the same, but the real forces contributing to it change with position.
Does centripetal force do work?
In uniform circular motion, the centripetal force is perpendicular to the object's instantaneous displacement. Since work is W = Fs cos θ and θ = 90°, the centripetal force does no work.
This does not mean that no force acts or that no energy is involved. It means the purely radial force changes the direction of velocity without changing its magnitude, so the object's kinetic energy remains constant.
In non-uniform circular motion, the net force can also have a tangential component. That component changes the object's speed and can do work, while the radial component changes the direction of motion. Distinguishing radial and tangential components prevents the incorrect claim that forces never do work during circular motion.
An exam-focused method for centripetal force questions
Use the following method whenever a question involves turning, orbiting, or looping motion:
- Identify the circular path. Locate its centre and determine the correct radius.
- Draw the real forces. Do not add centripetal force as an extra interaction.
- Choose inward as the radial direction. This usually makes the equation easier to interpret.
- Write the radial force equation. Use
ΣF_inward = mv²/ror an equivalent angular form. - Resolve angled forces. Only radial components contribute to the centripetal resultant.
- Substitute in SI units. Check that speed is in
m s⁻¹, mass inkg, and radius inm. - State a direction with the answer. A centripetal force is directed toward the centre.
- Check physical sense. Greater speed should require a much larger inward force when mass and radius are fixed.
A strong explanation might state: “The object's speed is constant, but its velocity changes because its direction changes. It therefore has an acceleration toward the centre, so Newton's second law requires a resultant force in the same direction.” This is more complete than saying only that a force “keeps it moving in a circle.”
After learning the method, use the A.2.4 Circular Motion Questionbank to practise identifying the real inward forces. The broader IB Physics Questionbank is useful once you are ready to distinguish circular-motion problems from other mechanics questions without being told which equation to use.
Common mistakes to avoid
- Adding centripetal force to a free-body diagram: Draw tension, gravity, friction, and other real forces instead.
- Drawing velocity toward the centre: Velocity is tangent to the path; acceleration and radial resultant are inward.
- Calling centripetal force an outward force: The inward force is centripetal. An apparent outward effect is associated with inertia or a centrifugal force introduced in a rotating frame.
- Assuming constant speed means zero acceleration: Velocity changes whenever its direction changes.
- Using diameter instead of radius: The equations require the distance from the object to the centre of curvature.
- Ignoring other radial forces: At the bottom of a loop, for example, the inward resultant is
N - mg, not justN. - Forgetting that speed is squared: A modest increase in speed can produce a much larger force requirement.
- Using a surface altitude as orbital radius: For an orbit, use the centre-to-centre distance, commonly
r = R + h. - Confusing a Newton's third-law pair: Centripetal and centrifugal forces are not an action-reaction pair. Third-law forces act on different objects.
For rapid terminology checks, the RevisionDojo IB Physics glossary can help you distinguish force, acceleration, angular speed, and related terms. Jojo AI can also examine your force equation or free-body diagram reasoning, but you should still state explicitly which physical forces form the inward resultant.
Conclusion
Centripetal force is the inward resultant force required for circular motion, with magnitude F_c = mv²/r = mω²r in uniform circular motion. It is not a new force to add to a diagram; it is a role performed by real forces such as gravity, tension, friction, or the normal force.
For IB exams, mark the centre, draw only real forces, and write ΣF_inward = mv²/r. Keep velocity tangential, acceleration inward, and centrifugal force separate from an inertial-frame free-body diagram. RevisionDojo's circular-motion Study Notes, Questionbank, and Jojo AI are most useful when combined in that order: understand the model, apply it to questions, and then diagnose any remaining errors.
Sources and referenced URLs
- Official IB Physics subject brief, first assessment 2025
- NASA centripetal force classroom resource
- OpenStax University Physics: Centripetal Force
- IB Physics Circular Motion and Gravitation Explained
- RevisionDojo A.2.4 Circular Motion notes
- RevisionDojo A.2.4 Circular Motion Questionbank
- RevisionDojo IB Physics Questionbank
- RevisionDojo IB Physics glossary