AP Physics 1 Review

AP Physics Full Review: Past Exam Breakdown

• Key Topic Breakdown of Exam Content:

  • Energy (25%)

  • Dynamics/Newton's Law (20%)

  • Kinematics (17%)

  • Rotational Motion (16%)

  • Momentum (14%)

  • Circular Motion/Gravitation (5%)

  • Simple Harmonic Motion (3%)

• Study Tip: Focus on vocabulary, definitions, and formulas as key components for success in physics exams.

Kinematic Equations and Motion Graphs

• Graphs Understanding:

  • In a position graph, the slope represents velocity.

  • In a velocity graph, the slope indicates acceleration and the area under the curve represents displacement.

  • In an acceleration graph, the area under the line represents velocity.

• Basic Formulas:

  • Acceleration: $a = \frac{\Delta v}{\Delta t}$

  • Velocity (general): $v = \frac{d}{t}$

  • Average Velocity: V1+V2/2

Projectile Motion

• Basic Principles:

  • Horizontal Motion: characterized by velocity, displacement, and time.

  • Vertical Motion: characterized by initial velocity, final velocity, displacement, time, and acceleration.

  • Key Connection: The horizontal time is equal to the vertical time.

  • Use kinematic equations first to derive vertical quantities, then apply them to find horizontal quantities.

  • At the highest point of a projectile's path, $t = \frac{-V_{oy}}{-g}$.

• Including Angles:

  • Decompose projectile motion into horizontal and vertical components.

  • Apply kinematics: for projectile motion problems, use the average velocity equation for horizontal quantities, $V = \frac{d}{t}$.

  • If launched at an angle, utilize sine for vertical displacement and cosine for horizontal displacement:

  • Horizontal range: $R = \frac{V_{oy}^2 \sin(2\theta)}{g}$, where $\theta$ is the launch angle.

Forces and Newton's Laws

• Newton’s Laws of Motion:

  1. An object at rest will remain at rest unless acted upon by a net force; an object in motion maintains its velocity unless acted upon by a net force.

  2. The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass: $a = \frac{F_{net}}{m}$.

  3. For every action, there is an equal and opposite reaction (involves two forces acting on two objects).

• Equilibrium Concepts:

  • Static Equilibrium: Occurs when the net force is zero for a motionless system.

  • Dynamic Equilibrium: Occurs when the net force is zero for a moving system (no acceleration, constant velocity).

  • If an object is not accelerating, all forces must be balanced.

• Normal Force and Friction:

  • Normal Force (Fn): Acts perpendicular to the contact surface, calculated typically as $F_{g} = mg$.

  • Friction Force (Ff): Acts parallel to the contact surface:

  • Static Friction ($F<em>{s}$): Resists the start of motion and is dependent on the applied force until the maximum is reached: Fs < \mus Fn.

  • Kinetic Friction ($F<em>{k}$): Acts on moving objects: $F</em>k = \mu<em>k F</em>n$.

• Slope Components in Forces:

  • Use sine components to describe sliding motion and cosine components to maintain object proximity to the ramp, $cos$ into the ramp, and $sin$ going downwards.

Atwood Machines and Tension Analysis

• System Description:

  • Two masses are connected by a massless string over a massless frictionless pulley.

  • Tension is uniform across the string.

  • Both masses will have equal acceleration, $F_{net} = ma$ and tension analysis yields:

  • $T = m_{g} - ma$.

  • Conditions for equilibrium are indicated when $m<em>1 + m</em>2$ leads to equilibrium; otherwise, acceleration occurs.

• Key Motion Concepts:

  • For an object sliding down a frictionless ramp, the end velocity can be determined using $v = \sqrt{2gh}$.

Work, Energy, and Power

• Work Defined:

  • Work (W) is the energy transfer to or from an object by means of force causing a displacement.

  • It is a scalar quantity, defined by the formula: $W = Fd \cos(\theta)$ or alternatively $W = KE<em>f - KE</em>i$.

• Work Classifications:

  • Positive Work: Adds mechanical energy when the force and displacement are in the same direction (0° < Θ < 90°).

  • Negative Work: Extracts mechanical energy when the force and displacement are in opposite directions (90° < Θ < 180°).

  • Zero Work: Occurs when force is perpendicular to the direction of motion.

• Energy Types:

  • Kinetic Energy (KE): Energy of motion, given by $KE = \frac{1}{2}mv^2$ (if KE is doubled, velocity increases by $\sqrt{2}$).

  • Potential Energy (PE): Energy based on position, specifically gravitational potential energy: $U_g = mgh$.

  • Gravitational PE relates to height, where $\frac{1}{2}v^2 = gh$ due to mass cancelling out when frictionless.

  • Elastic Potential Energy is defined as: $U_s = \frac{1}{2}kx^2$ where k is spring constant.

• Conservation Laws:

  • Total energy in an isolated system remains constant; mechanical energy is conserved absent friction.

  • Work is required to change the total mechanical energy of a system.

• Power Defined:

  • Power (P) measures the rate of energy change or working: $P = \frac{W}{t}$ (measured in watts, with $1 W = 1 J/s$).

  • Extended calculations: $P = Fv \cos(\theta)$ can connect force, velocity, and angle to power interpretation.

Momentum and Impulse

• Momentum (p): Defined as the tendency for an object to remain in motion, momentum is conserved in isolated systems. Momentum is related by:

  • $p = mv$.

• Impulse (J): Change in momentum of an object, defined by:

  • $J = F \Delta t = \Delta (mv)$.

• Impulse is represented graphically as the area under a force vs. time graph.

• Collision Types:

  • Elastic Collisions: Both momentum and kinetic energy conserved; often seen in hard collisions where objects bounce off.

  • Conservation Law: $P<em>{1i} + P</em>{2i} = P<em>{1f} + P</em>{2f}$.

  • Inelastic Collisions: Only momentum is conserved; objects may stick together post-collision but kinetic energy is not conserved.

  • Explosions: Begin as a single object and split into parts without conserving kinetic energy but do conserve momentum.

Center of Mass, Systems

• Center of Mass (CM): Balance point in a system, mathematically determined by:

  • Establish a coordinate point ($x=0$) and for each component multiply its mass by its distance, summing these and dividing by total mass.

• System Types:

  • Open systems swap energy up/down with surroundings.

  • Closed systems conserve energy without external energy change; friction indicates an open system, while mechanical energy is conserved when friction is absent.

Circular Motion and Gravitation

• Uniform Circular Motion Characteristics:

  • It's where an object moves in a circular path at constant tangential speed, while continuously changing its direction.

  • Tangential Speed (v): Remains consistent; tangential velocity varies due to direction change.

• Centripetal Motion Dynamics:

  • Centripetal Acceleration (Aₙ): Always directed towards the center: $A_c = \frac{v^2}{r}$.

  • Centripetal Force (F_c): Required to maintain circular motion and is given by:

  • $F<em>c = m \frac{v^2}{r}$ or $F</em>c = mw^2r$ for circular motion on a string.

  • For planetary orbits, gravitational force acts as centripetal force.

• Gravitation Principles:

  • Newton’s Law of Universal Gravitation:

  • $F<em>g = \frac{G m</em>1 m_2}{r^2}$, where G is the gravitational constant (6.67 x 10^-11).

  • Gravitational Field Strength (g): Field strength defined as $g = \frac{GM}{r^2}$ (9.81 m/s² at Earth's surface).

  • Gravitational Potential Energy (Ug): Potential energy between two masses given by $U<em>g = \frac{G m</em>1 m_2}{r}$.

Rotational Motion Basics

• Rotational Dynamics and Quantities:

  • Translational vs. Angular Motion:

  • Translational: moves across space; Angular: rotates.

  • Rotational motion combines aspects of both.

  • Angular Velocity (ω): defined as the angle/time period.

• Angular Acceleration (α): Rate of change in angular velocity; defined through:

  • $α = \frac{\Delta \omega}{t}$.

• Torque (T): Defined as the force that causes rotational motion, given by:

  • $T = F r \sin(θ)$ where θ is the angle between lever arm and applied force. The unit is Newton-meters (N·m).

• Equilibrium in Rotational Mechanics:

  • Rotational equilibrium occurs when net torque is zero, analyzed similarly to net force considerations in translational equilibrium.

Simple Harmonic Motion (SHM)

• Foundational Concepts:

  • SHM is characterized by a restoring force proportional to displacement from equilibrium.

  • Key definitions include:

  • Amplitude (A): Maximum displacement.

  • Period (T): Time for one full cycle, given as $T = 2π√(m/k)$ for mass-spring systems.

  • Frequency (f): Cycles per time: $f = \frac{1}{T}$.

• Hooke's Law: Describes restoring force in terms of displacement and spring constant:

  • $F_s = kx$.

  • Restoring Forces: These forces bring the system back to equilibrium point.

Waves and Sound

• Parts of Transverse Waves:

  • Crests and Troughs: Maximum displacements above and below equilibrium, respectively.

  • Wavelength (λ): Distance between successive crests or troughs.

  • Amplitude and Frequency: Key features defining wave properties.

• Wave Speed: Described by:

  • $v = fλ$ and $v = \frac{d}{t}$.

  • Constant wave speeds depend on medium characteristics, independent of frequency.

• Superposition and Interference:

  • When two waves overlap, their displacements combine algebraically.

  • Constructive and Destructive Interference: Describes how waves interact and form new wave patterns.

• Doppler Effect: Observed when a wave source moves relative to an observer, altering perceived frequency:

  • Higher frequency when moving closer, lower when moving apart.

Electric Forces and Fields

• Basic Concepts of Charge:

  • Atoms contain protons, neutrons and electrons; charge is conserved.

  • Ionic Charge: Produced by imbalance in protons and electrons (adding/removing electrons changes total charge).

• Coulomb’s Law: Governs the interaction of charged particles:

  • $F<em>E = k \frac{|q</em>1 q_2|}{r^2}$.

  • States that electric force is attractive for unlike charges and repulsive for like charges.

• Electric Field (E): Related to the charge and force experienced by a test charge:

  • $E = \frac{F}{q}$,

  • Field strength inversely correlates with the distance from the charge, with denser field lines indicating stronger fields.

• Superposition Principle: The resultant electric field is the vector sum of all individual fields.

Direct Current Circuits

• Electric Current Concept: Defined as the flow of electric charge:

  • Measure of charge crossing a plane per time: $I_{avg} = \frac{∆Q}{∆t}$ (1 A = 1 C/s).

  • Current direction conventionally taken as flow of positive charge.

• Resistance is analogous to flow obstruction, defined by Ohm’s Law:

  • $R = \frac{V}{I}$ and also reducible via $R = \frac{\rho L}{A}$ with $\rho$ as resistivity.

• Electric Circuit Elements:

  • Emf represents work per charge; voltage provides energy to charges.

• Circuit Analysis and Kirchhoff's Rules:

  • Momentum through junctions must balance, total potential must sum to zero in closed loops.

  • Analyze volts dropped/increased across components based on current direction and resistive properties.

In physics, the magnitude of a vector quantity refers to its size or strength without regard to its direction. To solve for the magnitude of a vector, you typically apply the Pythagorean theorem if you have the vector's components. The basic formula for finding magnitude is:
$|V| = \sqrt{V<em>x^2 + V</em>y^2}$
where:

• $|V|$ is the magnitude of the vector V.

• $V_x$ is the horizontal component of the vector.

• $V<em>y$ is the vertical component of the vector. For three-dimensional vectors, the formula extends to: $|V| = \sqrt{V</em>x^2 + V<em>y^2 + V</em>z^2}$
  where $V_z$ is the vertical component in three dimensions.