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AP Course

AP Physics 1

Updated for the AP Physics 1 framework effective fall 2024, including mechanics, rotation, oscillations, and fluids.

Study every current unit through original concept lessons, formula derivations, experiments, quizzes, and practice sets.

Lessons
Scalars and Vectors in One DimensionDisplacement, Velocity, and AccelerationRepresenting MotionReference Frames and Relative MotionVectors and Motion in Two DimensionsSystems and Center of MassForces and Free-Body DiagramsNewton's Third LawNewton's First LawNewton's Second LawGravitational ForceKinetic and Static FrictionSpring 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 OscillatorsInternal Structure and DensityPressureFluids and Newton’s LawsFluids and Conservation Laws
Quizzes
Practice Problems Formula notes, diagrams, and practice sets will be added here.

AP Physics 1 · Unit 6 · Topic 6.5

Rolling

Energy and angular momentum connect torque, rotation rate, distribution of mass, and rolling motion.

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.

\[K_{\text{rot}}=\frac12I\omega^2\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. A particle's speed in a rigid rotation is v=rω.
  2. Substitute v=rω into each particle's ½mv² and sum.
  3. The sum of mr² is I, leaving ½Iω².
\[W=\Delta K_{\text{rot}}=\frac12I(\omega_f^2-\omega_i^2)\]

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

A wheel has I=2 kg·m² and ω=3 rad/s. Find its rotational kinetic energy.

Answer: Krot=½(2)(3²)=9 J.

Investigation idea: Roll objects with different mass distributions down the same ramp and compare arrival times and energy partitions.

Common trap: Do not use translational kinetic energy alone for a rolling rigid body.

Checkpoint · Topic 6.5

Explain how rolling supports or limits this conclusion: Krot=½(2)(3²)=9 J.

Official curriculum reference: College Board AP Physics 1 course page. The explanation and worked example are independently written for this study site.