IInsomniaStudyroom
Focus music
Pomodoro
25:00

AP Course

AP Physics C: Mechanics

Updated for the AP Physics C: Mechanics framework effective fall 2024, with calculus-based derivations, labs, quizzes, and practice.

Build calculus-based mechanics with original derivations, experiments, quizzes, and practice sets.

Lessons
Scalars and VectorsDisplacement, Velocity, and AccelerationRepresenting MotionReference Frames and Relative MotionMotion in Two or Three DimensionsSystems and Center of MassForces and Free-Body DiagramsNewton’s Third LawNewton’s First LawNewton’s Second LawGravitational ForceKinetic and Static FrictionSpring ForcesResistive ForcesCircular MotionTranslational Kinetic EnergyWorkPotential EnergyConservation of EnergyPowerLinear MomentumChange in Momentum and ImpulseConservation of Linear MomentumElastic and Inelastic CollisionsRotational KinematicsConnecting Linear and Rotational MotionTorqueRotational InertiaRotational Equilibrium and Newton’s First Law in Rotational FormNewton’s Second Law in Rotational FormRotational Kinetic EnergyTorque and WorkAngular Momentum and Angular ImpulseConservation of Angular MomentumRollingMotion of Orbiting SatellitesDefining Simple Harmonic Motion (SHM)Frequency and Period of SHMRepresenting and Analyzing SHMEnergy of Simple Harmonic OscillatorsSimple and Physical Pendulums
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics C: Mechanics · Unit 6 · Topic 6.5

Rolling

Rotational work-energy and angular impulse connect changing mass distribution, torque, and rolling constraints.

1. Topic Lens

Rolling is studied through energy and momentum of rotating systems. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[\vec\tau_{\text{ext}}=\frac{d\vec L}{dt}\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. Angular momentum changes according to external torque.
  2. If external angular impulse is negligible, integrate τext=0 to obtain constant L.
  3. For a rigid body about a fixed principal axis, L=Iω.
\[L_i=L_f\Rightarrow I_i\omega_i=I_f\omega_f\]

3. Detailed Visual Model

Pixel diagram for RollingOriginal schematic connecting Rolling to Energy and Momentum of Rotating Systems.
Rolling: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

An isolated rotating object halves its rotational inertia. What happens to ω?

Answer: Conservation of angular momentum requires the angular speed to double.

Investigation idea: Use a low-friction rotating platform with movable masses to test Iω conservation and energy change.

Common trap: Angular momentum can be conserved while rotational kinetic energy changes due to internal work.

Checkpoint · Topic 6.5

Explain how rolling supports or limits this conclusion: Conservation of angular momentum requires the angular speed to double.

Official curriculum reference: College Board AP Physics C: Mechanics course page. The explanation and worked example are independently written for this study site.