Centripetal acceleration is the center-pointing acceleration of any object moving along a circular path, with magnitude a = v²/r (or a = ω²r), caused by the continuous change in the direction of the velocity vector even when speed is constant.
Centripetal acceleration is what you get when velocity changes direction instead of magnitude. An object moving in a circle at constant speed is still accelerating, because acceleration is the rate of change of the velocity vector, and that vector is constantly rotating to stay tangent to the circle. The acceleration always points toward the center of the circle ("centripetal" literally means center-seeking), and its magnitude is a = v²/r, where v is the object's speed and r is the radius of the path.
In AP Physics C, you should also know the angular version, a = ω²r, since problems often hand you angular velocity instead of linear speed. And here's the calculus payoff for this course: if you write the position of an object in uniform circular motion as a vector and differentiate twice, the v²/r result falls right out. The acceleration vector you get points opposite to the position vector, which is the mathematical proof that it aims at the center. If the object is also speeding up or slowing down, it has a tangential acceleration component too, and the centripetal piece only accounts for the direction change.
Centripetal acceleration lives in Topic 2.2 (Circular Motion), inside the dynamics unit, and it's the bridge between kinematics and Newton's second law for anything that turns. Once you can write a = v²/r, every circular motion problem becomes a standard F = ma problem with one twist. You sum the real forces along the radial direction and set that net force equal to mv²/r. Cars on banked curves, masses on strings, satellites in orbit, and loops on roller coasters all run through this single equation. It also resurfaces later in the course whenever rotation or gravitation shows up, so the time you invest here pays off across multiple units.
Keep studying AP Physics C: Mechanics Unit 2
Centripetal Force (Unit 2)
Centripetal force is just Newton's second law applied to centripetal acceleration. It's not a new force on your free-body diagram; it's the net radial force (tension, gravity, friction, normal force, or some combination) that equals mv²/r. Acceleration is the kinematic fact, force is the dynamic cause.
Velocity (Unit 1)
Centripetal acceleration exists precisely because velocity is a vector. In uniform circular motion the speed never changes, but the direction of v changes continuously, and that direction change is an acceleration. This is the single best example for testing whether you really understand vectors versus scalars.
Angular Velocity (Ω) (Unit 2)
Since v = ωr for circular motion, you can rewrite a = v²/r as a = ω²r. Problems about rotating platforms, spinning amusement park rides, or anything described in rad/s expect you to switch fluently between the two forms.
Normal Force and Friction (Unit 2)
On a flat curve, static friction supplies the centripetal acceleration, so the maximum safe speed comes from μmg = mv²/r. On a banked curve or at the top of a loop, the normal force takes over part or all of the job. These setups are classic AP problems because they force you to identify which real force points toward the center.
Circular motion shows up in both multiple choice and free response, almost always disguised as a Newton's second law problem. MCQ stems test the concept directly, asking which way the acceleration points (toward the center, always) or how a changes when you double v or halve r (a quadruples with v, doubles when r is halved). FRQs typically give you a physical setup, like a car on a banked curve, a ball on a string, or a block on a rotating turntable, and ask you to draw a free-body diagram, apply ΣF = mv²/r along the radial direction, and solve for a speed, tension, friction coefficient, or minimum radius. The most common point-loser is drawing a fake "centripetal force" arrow on the free-body diagram. Only draw real forces, then set their radial sum equal to mv²/r. For Physics C specifically, be ready to derive a = v²/r from position vectors using calculus, since derivation questions reward students who can build the result, not just quote it.
Centripetal acceleration is the kinematic quantity (a = v²/r, pointing at the center). Centripetal force is whatever net real force produces that acceleration. The trap is treating "centripetal force" as its own force and adding it to a free-body diagram alongside tension or gravity. It isn't a separate force. It's a label for the radial component of the net force you already drew. Diagram the real forces, then write ΣF_radial = mv²/r.
Centripetal acceleration always points toward the center of the circular path, perpendicular to the velocity vector.
Its magnitude is a = v²/r in terms of speed, or a = ω²r in terms of angular velocity, and you should be able to use both forms.
An object in uniform circular motion is accelerating even at constant speed, because the direction of the velocity vector is constantly changing.
Centripetal acceleration is caused by real forces like tension, friction, gravity, or the normal force, never by a separate "centripetal force" you add to a diagram.
If speed doubles, centripetal acceleration quadruples; if radius doubles at the same speed, centripetal acceleration is cut in half.
When an object speeds up or slows down on a circle, total acceleration has both a centripetal (radial) component and a tangential component.
It's the acceleration of any object moving in a circle, directed toward the center of the circle, with magnitude a = v²/r or equivalently a = ω²r. It exists because the velocity vector changes direction continuously, even if speed stays constant.
Yes. Acceleration is the rate of change of the velocity vector, not just speed. In uniform circular motion the speed is fixed but the direction changes every instant, so there's a nonzero acceleration of v²/r pointing at the center.
Centripetal acceleration is the kinematic quantity (v²/r toward the center); centripetal force is the net real force causing it, equal to mv²/r by Newton's second law. On the exam, never draw "centripetal force" as its own arrow on a free-body diagram. Draw the actual forces like tension or friction instead.
No. Centripetal acceleration is real and points toward the center. The "centrifugal" outward push is a fictitious effect you feel only in a rotating reference frame, and it earns zero credit if you cite it in an inertial-frame FRQ solution.
Centripetal acceleration points toward the center and changes the velocity's direction; tangential acceleration points along the path and changes the speed. In nonuniform circular motion both exist at once, and the total acceleration is their vector sum.
Connect this key term to the AP exam workflow: review the course, practice questions, and check related study tools.
Review units, study guides, and course resources.
Check this vocabulary in multiple-choice context.
Apply key concepts in written AP responses.
Estimate the exam score you are working toward.
Review the highest-yield facts before practice.
Put the full course together before test day.