AP Physics 2: Algebra-Based Study Guide

1. Introduction to AP Physics 2

AP Physics 2 is a continuation of AP Physics 1 and focuses on topics such as fluid mechanics, thermodynamics, electricity and magnetism, optics, and modern physics. It emphasizes problem-solving and understanding fundamental concepts through inquiry-based learning.

Exam Format:

Multiple-choice questions: Assess knowledge of concepts and problem-solving.
Free-response questions: Apply knowledge to solve problems involving real-world scenarios.

2. Fluids

Properties of Fluids:

Density (ρ): The mass per unit volume, ρ = m / V.
Pressure (P): The force per unit area, P = F / A.
Hydrostatic Pressure: The pressure at a given depth in a fluid is P = ρgh, where g is the acceleration due to gravity and h is the height of the fluid.

Buoyancy:

Archimedes' Principle: A fluid exerts an upward buoyant force equal to the weight of the displaced fluid.
Buoyant Force (Fₓ): Fₓ = ρfluid * Vdisplaced * g, where Vdisplaced is the volume of displaced fluid.

Fluid Flow:

Continuity Equation: A1v1 = A2v2, where A is the cross-sectional area and v is the velocity of the fluid. The flow rate is constant for an incompressible fluid.
Bernoulli’s Equation: P + ½ρv² + ρgh = constant, describes the conservation of energy in a fluid system.

3. Thermodynamics

Temperature and Heat:

Temperature (T): A measure of the average kinetic energy of particles in a substance.
Heat (Q): Energy transferred between objects due to temperature differences. Q = mcΔT, where m is mass, c is specific heat capacity, and ΔT is the change in temperature.

Laws of Thermodynamics:

Zeroth Law: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
First Law (Conservation of Energy): ΔU = Q - W, where ΔU is the change in internal energy, Q is heat added, and W is work done by the system.
Second Law: The total entropy of an isolated system always increases over time. This implies that heat naturally flows from hot to cold.
Third Law: As the temperature approaches absolute zero, the entropy of a system approaches a minimum.

Heat Engines:

Efficiency: η = W / Qh, where W is the work done by the engine, and Qh is the heat absorbed from the hot reservoir.
Carnot Efficiency: The maximum possible efficiency of a heat engine, η = 1 - Tc / Th, where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.

4. Electrostatics

Coulomb’s Law:

F = kₑ |q₁q₂| / r², where kₑ is Coulomb's constant, q₁ and q₂ are the charges, and r is the distance between them.

Electric Field (E):

E = F / q, where F is the force on a test charge q in the field.
The electric field created by a point charge is E = kₑ q / r².

Electric Potential Energy (U):

U = kₑ q₁q₂ / r, the potential energy between two charges.

Capacitance (C):

C = Q / V, where Q is the charge stored and V is the potential difference.

Energy Stored in a Capacitor:

U = ½CV², the energy stored in a capacitor with capacitance C and voltage V.

5. Magnetism

Magnetic Fields:

The magnetic field around a magnetic object is represented by magnetic field lines. The direction of the magnetic field is the direction in which the north pole of a compass needle points.
Magnetic Force on a Moving Charge: F = qvB sin(θ), where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and magnetic field.

Biot-Savart Law:

Describes the magnetic field produced by a current-carrying wire: B = (μ₀ / 4π) * (I dL × r̂) / r².

Ampère's Law:

The magnetic field around a current-carrying wire is related to the current by the integral form of Ampère's law: ∮B · dl = μ₀I.

Magnetic Force on a Current-Carrying Wire:

F = I L B sin(θ), where I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the wire and magnetic field.

6. Electromagnetic Induction

Faraday’s Law of Induction:

The induced EMF (electromotive force) in a closed loop is proportional to the rate of change of magnetic flux through the loop: ε = -dΦ / dt.

Lenz’s Law:

The direction of the induced current is such that it opposes the change in magnetic flux that caused it.

Inductance (L):

The property of a coil or solenoid that resists changes in current. The inductance of a coil is L = NΦ / I, where N is the number of turns, Φ is the magnetic flux, and I is the current.

7. Optics

Reflection and Refraction:

Law of Reflection: θ₁ = θ₂, the angle of incidence equals the angle of reflection.
Snell’s Law (Refraction): n₁ sin(θ₁) = n₂ sin(θ₂), where n is the refractive index of the medium and θ is the angle of incidence or refraction.

Lenses and Mirrors:

Lens Equation: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
Magnification (m): m = -di / do.

Wave Behavior in Optics:

Interference: Constructive interference occurs when two waves are in phase, and destructive interference occurs when two waves are out of phase.
Diffraction: The bending of light around obstacles, resulting in interference patterns.

8. Modern Physics

Photoelectric Effect:

The emission of electrons from a metal surface when light shines on it. The energy of the emitted electrons is E = hf - φ, where h is Planck’s constant, f is the frequency of the incident light, and φ is the work function of the metal.

Quantum Theory:

Energy Quantization: E = nhf, where n is an integer, h is Planck’s constant, and f is the frequency of the radiation.
Wave-Particle Duality: Matter and radiation exhibit both wave-like and particle-like properties.

Special Relativity:

Time Dilation: Δt' = Δt / √(1 - v²/c²), where Δt' is the time interval measured by a moving observer, Δt is the time interval measured by a stationary observer, v is the velocity, and c is the speed of light.
Length Contraction: L' = L √(1 - v²/c²), where L' is the contracted length and L is the rest length.