Calculus in Physics: every key term you need

Physics C Unit 1

Advanced mechanics and electricity/magnetism using calculus; rigorous mathematical treatment.

Calculus in Physics

Derivatives: rate of change; integrals: accumulation; essential for precise physical descriptions.

Force and Acceleration

F = ma; F_net = m(dv/dt); applies to any force; foundation of mechanics; vector equation.

Work and Kinetic Energy

W = ∫F·ds; ΔKE = W (work-energy theorem); power P = dW/dt = F·v; energy transfer rate.

Potential Energy

Conservative forces have PE; U = -∫F·ds; total mechanical energy E = KE + PE conserved if only conservative forces.

Center of Mass

x_cm = Σm_i x_i/Σm_i; system motion described by CM; internal forces don't affect CM motion.

Rotational Kinematics

Angular velocity ω = dθ/dt; angular acceleration α = dω/dt; θ = θ₀ + ω₀t + (1/2)αt² (rotational equations).

Torque

τ = r×F; produces angular acceleration; τ = Iα; net torque = moment of inertia × angular acceleration.

Moment of Inertia

I = Σm_i r_i²; rotational analog of mass; depends on axis and mass distribution; greater distance = greater I.

Angular Momentum

L = Iω; conserved if net torque = 0; L = r×p for point particle; fundamental conserved quantity.

Oscillations

x = A cos(ωt+φ); SHM for springs and pendulums; ω = √(k/m) (spring), √(g/L) (pendulum); energy oscillates KE↔PE.

Waves

Travel through medium; v = fλ; energy propagation; superposition: waves add; interference, diffraction.

Electric Fields (Calculus)

E = -dV/dr; Gauss's law: ∮E·dA = Q_enc/ε₀; differential form: ∇·E = ρ/ε₀.

Magnetic Fields (Calculus)

Biot-Savart law: dB = (μ₀I/4π) dl×r/r³; Ampere's law: ∮B·dl = μ₀I_enc; differential form: ∇×B = μ₀J.

Electromagnetic Waves

Maxwell equations predict waves; c = 1/√(μ₀ε₀); E and B perpendicular; intensity ∝ E₀²; radiates from accelerating charges.

Circuits (Advanced)

RC circuits: τ = RC time constant; RL circuits: τ = L/R; LC circuits: oscillate at ω = 1/√(LC); energy exchanges.

Relativity Preview

Speed of light constant; relativity of simultaneity; time dilation; mass-energy equivalence E = mc².

Quantum Concepts

Planck constant h; photon energy E = hf; wave-particle duality; uncertainty principle Δx·Δp ≥ ℏ/2.

Problem Solving (Advanced)

Complex multi-part problems; combine concepts; derive relationships; communicate solutions clearly.

Approximations and Limits

Know when to use approximations; small angle: sin θ ≈ θ; first-order expansions; understand validity.

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