Comprehensive Physics I Study Notes: Motion, Forces, Energy, Fluids, and Thermodynamics

Physical Quantities, Units, and Measurement

SI Units and Scientific Notation

Physics relies on standardized units and notation for clarity and consistency in measurements and calculations.

• SI Units: The International System of Units (SI) is the standard for scientific measurements. Key base units include meter (m) for length, kilogram (kg) for mass, and second (s) for time.

• Scientific Notation: Used to express very large or small numbers as a product of a number and a power of ten. For example, $3.16 \times 10^7$ represents 31,600,000.

• Prefixes: Common prefixes include kilo ($10^3$), mega ($10^6$), giga ($10^9$), centi ($10^{-2}$), milli ($10^{-3}$), micro ($10^{-6}$), and nano ($10^{-9}$).

Dimensional Analysis

Dimensional analysis checks the consistency of equations and converts between units.

• Key Quantities: Length (m), Mass (kg), Time (s), Velocity (m/s), Acceleration (m/s2).

Vectors and Motion

Vectors and Their Components

Vectors have both magnitude and direction, essential for describing motion in physics.

• Vector Components: Any vector can be broken into x and y components using trigonometric functions:

• $A_x = A \cos \theta$

• $A_y = A \sin \theta$

• Vector Addition: Combine components to find resultant vectors.

One-Dimensional Motion

Describes motion along a straight line, using position, velocity, and acceleration.

• Displacement: $\Delta x = x_f - x_i$

• Average Velocity: $v_{avg} = \frac{\Delta x}{\Delta t}$

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

• Equations of Motion (constant acceleration):

• $v = v_0 + at$

• $x = x_0 + v_0 t + \frac{1}{2} a t^2$

• $v^2 = v_0^2 + 2a(x - x_0)$

Projectile and Two-Dimensional Motion

Projectile motion involves independent horizontal and vertical motions under gravity.

• Horizontal motion: $x = v_{0x} t$

• Vertical motion: $y = v_{0y} t - \frac{1}{2} g t^2$

• Velocity components: $v_x = v_{0x}$ (constant), $v_y = v_{0y} - g t$

• Range and maximum height can be calculated using these equations.

Forces and Newton's Laws

Types of Forces

• Contact Forces: Result from physical contact (e.g., friction, tension).

• Field Forces: Act at a distance (e.g., gravity, electromagnetic).

Newton's Laws of Motion

• First Law (Inertia): An object remains at rest or in uniform motion unless acted on by a net force.

• Second Law: $F_{net} = m a$

• Third Law: For every action, there is an equal and opposite reaction.

Friction

• Static Friction: Prevents motion up to a maximum value $f_s \leq \mu_s N$

• Kinetic Friction: $f_k = \mu_k N$

Gravity and Weight

• Weight: $W = m g$

• Newton's Law of Universal Gravitation: $F_g = G \frac{M m}{r^2}$

Work, Energy, and Power

Work and Kinetic Energy

• Work: $W = F d \cos \theta$

• Kinetic Energy: $KE = \frac{1}{2} m v^2$

• Work-Energy Theorem: $W_{net} = \Delta KE$

Potential Energy

• Gravitational Potential Energy: $PE = m g h$

• Elastic Potential Energy (Spring): $PE_s = \frac{1}{2} k x^2$

Conservation of Energy

• Mechanical Energy Conservation: $KE_i + PE_i = KE_f + PE_f$ (if no non-conservative forces)

Power

• Average Power: $P = \frac{W}{t}$

Momentum and Collisions

Linear Momentum

• Momentum: $p = m v$

• Impulse: $J = F \Delta t = \Delta p$

Conservation of Momentum

• In a closed system, total momentum is conserved: $p_{i, total} = p_{f, total}$

Types of Collisions

• Elastic: Both momentum and kinetic energy are conserved.

• Inelastic: Momentum is conserved, but kinetic energy is not. Perfectly inelastic collisions involve objects sticking together.

Rotational Motion and Equilibrium

Rotational Kinematics

• Angular Displacement: $\Delta \theta$ (radians)

• Angular Velocity: $\omega = \frac{\Delta \theta}{\Delta t}$

• Angular Acceleration: $\alpha = \frac{\Delta \omega}{\Delta t}$

• Relationship to Linear Quantities: $v = r \omega$, $a_t = r \alpha$

Rotational Dynamics

• Moment of Inertia: $I = \sum m r^2$ (depends on mass distribution)

• Torque: $\tau = r F \sin \theta$

• Newton's Second Law for Rotation: $\tau_{net} = I \alpha$

Rotational Kinetic Energy

• $KE_{rot} = \frac{1}{2} I \omega^2$

Angular Momentum

• $L = I \omega$

• Conservation: If $\tau_{net} = 0$, then $L$ is constant.

Equilibrium

• Translational: $\sum F_x = 0$, $\sum F_y = 0$

• Rotational: $\sum \tau = 0$

Solids, Fluids, and Elasticity

Density and Pressure

• Density: $\rho = \frac{m}{V}$

• Pressure: $P = \frac{F}{A}$

Elasticity

• Young's Modulus (Y): $Y = \frac{\text{stress}}{\text{strain}} = \frac{F/A}{\Delta L / L_0}$

• Shear Modulus (S): $S = \frac{F/A}{\Delta x / h}$

• Bulk Modulus (B): $B = -\frac{\Delta P}{\Delta V / V_0}$

Fluids in Equilibrium

• Hydrostatic Pressure: $P = P_0 + \rho g h$

• Pascal's Principle: Pressure applied to a confined fluid is transmitted undiminished throughout the fluid.

• Archimedes' Principle: Buoyant force equals the weight of the fluid displaced: $F_B = \rho_{fluid} V_{displaced} g$

Fluid Dynamics

• Equation of Continuity: $A_1 v_1 = A_2 v_2$ (for incompressible fluids)

• Bernoulli's Equation: $P + \frac{1}{2} \rho v^2 + \rho g y = \text{constant}$

Oscillations and Waves

Simple Harmonic Motion (SHM)

• Position: $x(t) = A \cos(\omega t + \phi)$

• Velocity: $v(t) = -A \omega \sin(\omega t + \phi)$

• Acceleration: $a(t) = -A \omega^2 \cos(\omega t + \phi)$

• Period: $T = \frac{2\pi}{\omega}$

• Frequency: $f = \frac{1}{T}$

• Spring-Mass System: $\omega = \sqrt{\frac{k}{m}}$

• Pendulum (small angle): $T = 2\pi \sqrt{\frac{l}{g}}$

Waves

• Wave Speed: $v = f \lambda$

• Types: Mechanical (require medium), Electromagnetic (do not require medium)

• Sound: Speed depends on medium's bulk modulus and density: $v = \sqrt{\frac{B}{\rho}}$

• Doppler Effect: Observed frequency changes due to relative motion of source and observer.

Thermal Physics and Thermodynamics

Temperature and Thermal Expansion

• Temperature Scales: Celsius, Kelvin ($T_K = T_C + 273.15$), Fahrenheit

• Thermal Expansion:

• Linear: $\Delta L = \alpha L_0 \Delta T$

• Area: $\Delta A = 2\alpha A_0 \Delta T$

• Volume: $\Delta V = \beta V_0 \Delta T$

Ideal Gas Law

• $PV = nRT$

• $R = 8.314$ J/(mol·K)

• Microscopic interpretation: $PV = Nk_B T$

Kinetic Theory of Gases

• Average kinetic energy per molecule: $\langle KE \rangle = \frac{3}{2} k_B T$

• Total internal energy (monatomic ideal gas): $U = \frac{3}{2} nRT$

Heat and Calorimetry

• Specific Heat: $Q = m c \Delta T$

• Heat Transfer by Conduction: $P = k A \frac{\Delta T}{L}$

Thermodynamic Processes

• Isobaric (constant P): $W = P \Delta V$

• Isochoric (constant V): $W = 0$

• Isothermal (constant T): $\Delta U = 0$, $Q = W$

• Adiabatic (no heat exchange): $Q = 0$, $\Delta U = -W$

First Law of Thermodynamics

• $\Delta U = Q - W$

Heat Engines and Second Law

• Heat Engine Efficiency: $e = \frac{W_{eng}}{Q_h} = 1 - \frac{Q_c}{Q_h}$

• Second Law: No engine can convert all absorbed heat into work; some must be expelled to a cold reservoir.

• Entropy: $\Delta S = \frac{Q_{rev}}{T}$

Sample Table: SI Prefixes

Prefix	Symbol	Factor
kilo	k	$10^3$
mega	M	$10^6$
giga	G	$10^9$
centi	c	$10^{-2}$
milli	m	$10^{-3}$
micro	μ	$10^{-6}$
nano	n	$10^{-9}$

Additional info:

• Some equations and context were inferred and expanded for clarity and completeness.

• Examples and applications were added to illustrate key concepts.