Centripetal acceleration is the acceleration directed toward the center of a circular path, with magnitude v²/r. In AP Physics 2 (Topic 12.2), it's what the magnetic force qvB produces on a charged particle moving perpendicular to a magnetic field, bending its path into a circle.
Centripetal acceleration is the acceleration any object has when it moves in a circle. It always points toward the center of the circle, and its magnitude is v²/r. It doesn't speed the object up or slow it down; it only changes the direction of the velocity.
In AP Physics 2, this idea comes back in Unit 12 with a new force playing the starring role. When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force F_B = qvB sin θ is always perpendicular to the velocity (12.2.B.2). A force that's always perpendicular to velocity is exactly the recipe for circular motion. So you set the magnetic force equal to ma_c, which gives qvB = mv²/r. Solve that and you get r = mv/(qB), the radius of the particle's circular path. That one equation is the workhorse of Topic 12.2 problems.
Centripetal acceleration is the bridge between mechanics and magnetism in Unit 12 (Magnetism and Electromagnetism). Learning objective 12.2.B asks you to describe the force a magnetic field exerts on a moving charge, and the most common payoff of that description is circular motion. Because F_B is perpendicular to v, the magnetic force can never change the particle's speed, only its direction. That means it does zero work and acts purely as a centripetal force. This is how mass spectrometers separate ions, how the charge-to-mass ratio gets measured, and why heavier ions trace bigger circles in the same field. If you can write qvB = mv²/r without hesitating, most of Topic 12.2's quantitative questions open right up.
Keep studying AP® Physics 2 Unit 12
F_B = qvB sin θ (Unit 12)
This is the force that supplies the centripetal acceleration. When v is perpendicular to B, sin θ = 1 and the force is maximum, constant in magnitude, and always perpendicular to the motion. That combination is exactly what produces uniform circular motion.
Radius of curvature (Unit 12)
Setting qvB equal to mv²/r and solving gives r = mv/(qB). Faster or heavier particles make bigger circles; stronger fields or bigger charges make tighter ones. Exam questions love asking you to compare radii for different particles in the same field.
Charge-to-mass ratio (Unit 12)
Rearranging qvB = mv²/r gives q/m = v/(rB). Measure the speed, the radius, and the field, and you've identified the particle. This is the physics behind mass spectrometry and a classic AP problem setup.
Circular motion (AP Physics 1 carryover)
Nothing about a_c = v²/r changes in Physics 2. What changes is who provides the center-pointing force. In Physics 1 it was tension or gravity or friction; in Unit 12 it's the magnetic force. Same template, new force.
Topic 12.2 questions test centripetal acceleration almost entirely through the equation qvB = mv²/r. Common multiple-choice stems give you a charged particle's circular radius in a known field and ask for the magnetic force, the speed, or the radius expression r = mv/(qB) in symbols. A favorite comparison question gives two ions with masses m and 2m entering the same field at the same speed and asks how their radii compare (the 2m ion's circle is twice as big, since r is proportional to m). Harder setups combine perpendicular E and B fields, where the particle curves only when the forces don't cancel, connecting this idea to the velocity selector. Your job on these problems is always the same. Identify the magnetic force as the centripetal force, write Newton's second law toward the center, and solve.
Centripetal acceleration (v²/r) is a kinematic description of any circular motion. Centripetal force is not a separate force on your free-body diagram; it's just the net force pointing toward the center, supplied by some real force. In Topic 12.2, the magnetic force qvB is the real force, and 'centripetal' is the job it's doing. If you draw a free-body diagram with both 'magnetic force' and 'centripetal force' as arrows, you've double-counted.
Centripetal acceleration points toward the center of the circular path and has magnitude v²/r.
A magnetic force on a charge moving perpendicular to the field is always perpendicular to the velocity, so it bends the path into a circle without changing the particle's speed.
Setting qvB = mv²/r gives the radius of the circular path, r = mv/(qB), the most-used equation in Topic 12.2.
Because the magnetic force is perpendicular to motion, it does zero work, so the particle's kinetic energy stays constant while it circles.
At the same speed and field, radius is proportional to mass and inversely proportional to charge, which is why mass spectrometers can separate ions by where they land.
Centripetal force is not its own force; in Unit 12 the magnetic force is the real force, and centripetal is just the role it plays.
It's the acceleration of an object moving in a circle, directed toward the center with magnitude v²/r. In Unit 12, the magnetic force F_B = qvB supplies it for a charged particle moving perpendicular to a magnetic field, which is why the particle travels in a circle.
No. The magnetic force is always perpendicular to the velocity, so it does zero work and the speed (and kinetic energy) stays constant. It only changes the direction of motion, which is exactly what centripetal acceleration means.
Centripetal acceleration (v²/r) describes the motion; centripetal force is whatever real force causes it. In Topic 12.2 the magnetic force qvB is that real force, so the equation qvB = mv²/r is just Newton's second law aimed at the center of the circle.
Set the magnetic force equal to the centripetal requirement, qvB = mv²/r, and solve to get r = mv/(qB). Bigger mass or speed means a bigger circle; bigger charge or field means a tighter one.
The more massive one, since r = mv/(qB) is proportional to mass. An ion with mass 2m and the same charge traces a circle with twice the radius of an ion with mass m, which is the principle behind mass spectrometry.
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