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AP Physics C Overview

Aug 31, 2025

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Overview

This lecture reviews all major topics of AP Physics C: Mechanics, focusing on kinematics, dynamics, energy, momentum, rotation, gravitation, and oscillations—summarizing core concepts, equations, and problem-solving strategies.

Vectors and Kinematics

  • Scalars have magnitude only; vectors have both magnitude and direction (e.g., displacement, velocity, acceleration).
  • Vector addition can be performed graphically or by adding components; use i, j, k notation for x, y, z components.
  • Vector magnitude: |V| = √(Vx² + Vy²).
  • Displacement (Δx) = x - x₀; difference from distance, which is scalar and path-dependent.
  • Position, velocity, and acceleration are related via derivatives: velocity = dx/dt, acceleration = dv/dt.
  • Kinematics equations (for constant acceleration, one dimension):
    1. v = v₀ + at
    2. x = x₀ + v₀t + ½at²
    3. v² = v₀² + 2a(x - x₀)
  • Typical units: m (meters), m/s (velocity), m/s² (acceleration).
  • Gravity (g) ≈ 9.8 m/s² (use 10 m/s² for simplicity).
  • Reference frames: Relative velocity = velocity of object - velocity of frame; acceleration is invariant across inertial frames.

Projectile Motion

  • Projectile motion is 2D with constant acceleration: ax = 0, ay = -g.
  • Decompose velocity: vx = v₀ cosθ, vy = v₀ sinθ.
  • At the highest point, vy = 0, vx constant throughout.
  • For projectiles launched/landing at same height, Δy = 0; for elevated launches, adjust analysis accordingly.

Center of Mass

  • For symmetric objects, center of mass (COM) lies at geometric center.
  • For point masses:
    x_com = Σ(mx)/Σm ; y_com = Σ(my)/Σm
  • For continuous distributions: r_com = ∫r dm / ∫dm; use λ = dm/dr for variable density.

Newton’s Laws and Forces

  • Newton’s 1st Law: Objects remain at rest or in uniform motion unless acted on by a net force.
  • Newton’s 2nd Law: ΣF = ma.
  • Newton’s 3rd Law: For every action, there is an equal and opposite reaction.
  • Gravitational force: Fg = G m₁m₂ / r².
  • Normal force (Fn): Perpendicular to surface, Fn = mg on flat surfaces.
  • Friction: f = μFn; static friction (not moving) and kinetic friction (sliding).
  • Spring force: Fs = -kx.
  • Centripetal force: Fc = mv²/r.
  • Drag force (air resistance): Often F_drag = bv; at terminal velocity mg = bv.

Work, Energy, and Power

  • Kinetic energy: K = ½mv².
  • Gravitational potential energy: Ug = mgh (relative to a reference).
  • Spring potential energy: Us = ½kx².
  • Work: W = ∫F·dx (include cosθ for angles).
  • Work-Energy Theorem: W = ΔK.
  • Conservation of energy: ΔK + ΔU = 0 (if only conservative forces act).
  • Power: P = dW/dt; average power = W/t; for constant force, P = F·v.

Linear Momentum

  • Momentum: p = mv.
  • Conservation: p_initial = p_final in a closed system.
  • Impulse: J = Δp = ∫F dt; for constant F, J = FΔt.
  • Newton’s 2nd Law: F = dp/dt.
  • Elastic collision: kinetic energy conserved; inelastic: KE not conserved, objects may stick together.

Rotation and Torque

  • Angular displacement: θ = s/r.
  • Angular velocity: ω = v/r; angular acceleration: α = a/r.
  • Rotational kinematics mirror linear equations (replace x,v,a with θ,ω,α).
  • Torque: τ = r × F = rF sinθ.
  • Rotational inertia (moment of inertia): I = Σmr²; varies by object’s shape and axis.
  • Parallel axis theorem: I = I_cm + Md².
  • Newton’s 2nd Law (rotation): Στ = Iα.

Rotational Energy and Angular Momentum

  • Rotational KE: K_rot = ½Iω².
  • Rolling motion: total KE = translational + rotational.
  • Work by torque: W = ∫τ dθ.
  • Angular momentum: L = r × p = Iω; torque causes change in angular momentum (τ = dL/dt).
  • Conservation: L_initial = L_final if no external torque.

Gravitation (Universal and Shell Theorem)

  • Universal gravity: Fg = Gm₁m₂/r².
  • Orbital velocity and radius: derived from centripetal force equals gravitational force (v²/r = GM/r²).
  • Gravitational potential energy (universal): U = –GMm/r.
  • Escape velocity: v_escape = √(2GM/r).
  • Shell theorem: No net gravitational force inside a uniform spherical shell.

Oscillations and Simple Harmonic Motion (SHM)

  • SHM: motion due to restoring force F = –kx.
  • Mass-spring period: T = 2π√(m/k).
  • Simple pendulum period: T = 2π√(l/g).
  • Physical pendulum: T = 2π√(I/mgd).
  • SHM equations: x(t) = A cos(ωt + φ), ω = √(k/m) for springs.
  • Energy in SHM: E_total = ½kA², alternates between KE and potential.
  • Damped SHM: amplitude decreases over time due to non-conservative forces.

Key Terms & Definitions

  • Scalar — quantity with magnitude only.
  • Vector — quantity with magnitude and direction.
  • Reference Frame — perspective from which motion is measured.
  • Center of Mass (COM) — average position of mass in a system.
  • Friction (μ) — resistance force, static (not moving) or kinetic (sliding).
  • Impulse (J) — change in momentum.
  • Torque (τ) — rotational equivalent of force.
  • Moment of Inertia (I) — rotational mass.
  • Angular Momentum (L) — Iω, rotational analog of linear momentum.
  • SHM — periodic motion with linear restoring force.

Action Items / Next Steps

  • Complete assigned practice problems for each topic.
  • Program useful equations into your calculator for quick reference.
  • Review and memorize the reference sheet equations, especially for kinematics, energy, and rotation.
  • Practice deriving and applying Newton's laws, conservation principles, and SHM formulas.

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