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AP Physics 1: Algebra-Based Study Guide

1. Introduction to AP Physics 1

AP Physics 1 is an algebra-based physics course that covers topics such as mechanics, waves, and simple circuits. It emphasizes the development of scientific reasoning, problem-solving skills, and the application of physics concepts to real-world situations.

Exam Format:

  • Multiple-choice questions: Assess knowledge of concepts and problem-solving abilities.
  • Free-response questions: Test ability to apply knowledge to solve complex problems and analyze data.

2. Kinematics

Position, Velocity, and Acceleration:

  • Position (x): The location of an object in space.
  • Velocity (v): The rate of change of position, v = Δx / Δt.
  • Acceleration (a): The rate of change of velocity, a = Δv / Δt.

Equations of Motion (Constant Acceleration):

  1. v = v₀ + at
  2. x = x₀ + v₀t + ½at²
  3. v² = v₀² + 2a(x - x₀)

Free Fall:

  • Acceleration due to gravity is approximately g = 9.8 m/s² (near Earth's surface).
  • Objects in free fall experience constant acceleration downward.

3. Dynamics

Newton’s Laws of Motion:

  1. First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion unless acted upon by an external force.
  2. Second Law: F = ma, the force on an object is equal to the mass of the object times its acceleration.
  3. Third Law: For every action, there is an equal and opposite reaction.

Forces:

  • Gravitational Force: Fₓ = mg
  • Frictional Force: f = μN, where μ is the coefficient of friction, and N is the normal force.
  • Tension: The force exerted by a rope or string.
  • Normal Force: The force exerted by a surface that is perpendicular to the object’s surface.

Applications:

  • Objects can experience multiple forces simultaneously, and you must use vector addition to find the resultant force.

4. Circular Motion and Gravitation

Circular Motion:

  • Centripetal Force: The force required to keep an object moving in a circle, Fₓ = mv² / r, where m is mass, v is velocity, and r is radius.
  • Centripetal Acceleration: aₓ = v² / r.

Universal Law of Gravitation:

  • Fₓ = G(m₁m₂) / r², where G is the gravitational constant, m₁ and m₂ are the masses of two objects, and r is the distance between them.

5. Work, Energy, and Power

Work:

  • W = Fd cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.

Kinetic Energy:

  • KE = ½mv², the energy of an object due to its motion.

Potential Energy:

  • Gravitational Potential Energy: PE = mgh, where m is mass, g is acceleration due to gravity, and h is height.
  • Elastic Potential Energy (Spring): PEₛ = ½kx², where k is the spring constant and x is the displacement from equilibrium.

Conservation of Energy:

  • Energy cannot be created or destroyed, only converted from one form to another. KE + PE = constant.

Power:

  • P = W / t, the rate at which work is done or energy is transferred.

6. Momentum and Impulse

Momentum:

  • p = mv, the product of an object’s mass and velocity.

Impulse:

  • J = FΔt = Δp, the change in momentum is equal to the impulse applied to an object.

Conservation of Momentum:

  • In an isolated system, total momentum is conserved: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'.

7. Simple Harmonic Motion

Simple Harmonic Motion (SHM):

  • Motion where the restoring force is proportional to displacement: F = -kx, where k is the spring constant, and x is displacement.

Period and Frequency:

  • The period T is the time it takes for one complete oscillation.
  • The frequency f = 1/T, the number of oscillations per second.

Energy in SHM:

  • The total mechanical energy in SHM is conserved and is the sum of kinetic and potential energy: E = ½kA², where A is the amplitude.

8. Waves and Sound

Wave Properties:

  • Wavelength (λ): The distance between two consecutive crests or troughs.
  • Frequency (f): The number of wave cycles per second.
  • Speed (v): The rate at which the wave propagates, v = fλ.

Types of Waves:

  • Transverse Waves: Oscillations are perpendicular to the direction of wave propagation (e.g., light waves).
  • Longitudinal Waves: Oscillations are parallel to the direction of wave propagation (e.g., sound waves).

Sound:

  • Sound is a longitudinal wave that requires a medium to travel through.
  • Speed of Sound: The speed of sound in air at room temperature is approximately 343 m/s.

Doppler Effect:

  • The change in frequency of a wave as the source or observer moves.

9. 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:

  • The electric field at a point is the force per unit charge: E = F / q.

Electric Potential Energy:

  • The potential energy associated with a charge in an electric field: U = kₑ (q₁q₂) / r.

Capacitance:

  • The ability of a system to store charge, C = Q / V, where Q is the charge and V is the potential difference.

10. DC Circuits

Ohm’s Law:

  • V = IR, where V is voltage, I is current, and R is resistance.

Power in Circuits:

  • P = IV, the power delivered by the source of electrical energy.

Series and Parallel Circuits:

  • Series: Resistances add: Rₜ = R₁ + R₂ + ….
  • Parallel: Inverse of the total resistance is the sum of the inverses: 1 / Rₜ = 1 / R₁ + 1 / R₂ + ….