Physics Ladder · College

Mechanics with Calculus

Mechanics again, now with derivatives and integrals, as in AP Physics C: Mechanics and university physics I: variable forces, drag, work integrals, potential energy curves, rotation of solid bodies and orbits.

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51 topics in 7 units. Builds on Physics 1: Motion, Forces and Energy, plus Calculus 1 from the Math Ladder. Leads to Electricity and Magnetism. Not sure this is the right course? Find your rung.

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Unit 1 Kinematics with Calculus

9 topics

Velocity and acceleration as derivatives, motion found by integrating, and motion in two and three dimensions.

  1. Velocity as a Derivative
  2. Acceleration as a Derivative
  3. Velocity and Position from Acceleration
  4. Deriving the Constant-Acceleration Equations
  5. Acceleration That Depends on Position
  6. Position, Velocity and Acceleration Vectors
  7. Projectiles with Calculus
  8. Relative Motion and Galilean Frames
  9. Tangential and Centripetal Acceleration

Unit 2 Forces with Calculus

6 topics

Time-varying forces, drag, banked curves, pulley constraints and the center of mass by integration.

  1. Motion Under a Time-Varying Force
  2. Linear Drag and Terminal Velocity
  3. Quadratic Drag
  4. Banked Curves With and Without Friction
  5. Constraints in Pulley Systems
  6. Center of Mass by Integration

Unit 3 Work and Energy with Calculus

9 topics

Work as an integral, potential energy from force and force from potential energy, and energy diagrams.

  1. Work by a Variable Force
  2. Work Along a Path
  3. The Work-Energy Theorem from Newton's Second Law
  4. Conservative Forces
  5. Potential Energy from Force
  6. Force from Potential Energy
  7. Potential Energy Diagrams
  8. Instantaneous Power
  9. Gravitational Potential Energy and Escape Speed

Unit 4 Momentum and Systems of Particles

5 topics

Impulse as an integral, collisions in two dimensions, systems of particles and rockets.

  1. Impulse as an Integral
  2. Solving Elastic Collisions
  3. Collisions in Two Dimensions
  4. Newton's Second Law for a System
  5. The Rocket Equation

Unit 5 Rotation of Rigid Bodies

11 topics

Moments of inertia by integration, torque and angular momentum as cross products, rolling, rotational collisions and equilibrium.

  1. Angular Velocity and Acceleration with Calculus
  2. Moment of Inertia by Integration
  3. The Parallel-Axis Theorem
  4. Torque as a Cross Product
  5. Rolling Dynamics
  6. From Skidding to Rolling
  7. Angular Momentum of a Particle
  8. Collisions with Rotation
  9. Work and Power in Rotation
  10. Gyroscopes and Precession
  11. Static Equilibrium Problems

Unit 6 Gravitation and Orbits

5 topics

Gravity of spheres, orbital energy, Kepler's laws from Newton's, and elliptical orbits.

  1. Gravity of a Spherical Body
  2. Orbital Energy
  3. Kepler's Second Law from Angular Momentum
  4. Kepler's Third Law from Newton
  5. Speed on an Elliptical Orbit

Unit 7 Oscillations with Calculus

6 topics

Simple harmonic motion as a differential equation, physical pendulums, damping and resonance.

  1. The Equation of Simple Harmonic Motion
  2. Amplitude and Phase from Starting Conditions
  3. Springs Hanging Vertically
  4. Simple and Physical Pendulums
  5. Damped Oscillations
  6. Driven Oscillations and Resonance
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