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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 5 · Topic 5.2

Connecting Linear and Rotational Motion

Calculus-based mass distribution and vector torque determine angular acceleration and equilibrium.

1. Topic Lens

Connecting Linear and Rotational Motion is studied through torque and rotational dynamics. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[I=\int r_\perp^2\,dm\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. A mass element dm at perpendicular radius r has tangential acceleration rα.
  2. Its tangential force creates torque r(rα dm)=r²α dm.
  3. Integrating gives τ=α∫r²dm=Iα for a fixed axis.
\[\sum\tau=I\alpha\]

3. Detailed Visual Model

Pixel diagram for Connecting Linear and Rotational MotionOriginal schematic connecting Connecting Linear and Rotational Motion to Torque and Rotational Dynamics.
Connecting Linear and Rotational Motion: an original pixel-style model. Use it as a schematic, not a literal scale drawing.

4. Worked Example and Lab Link

A rigid body with I=2 kg·m² experiences 6 N·m net torque. Find α.

Answer: α=6/2=3 rad/s².

Investigation idea: Measure angular acceleration for the same torque with movable masses and compare with calculated I.

Common trap: Rotational inertia depends on the chosen axis; mass alone is insufficient.

Checkpoint · Topic 5.2

Explain how connecting linear and rotational motion supports or limits this conclusion: α=6/2=3 rad/s².

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