Notes, summaries, assignments, exams, and problems for Physics

Science & the Universe                                                                                                                                       

Astronomy = study of celestial objects and their interactions.                                    

Scientific method: relies on observation, testing, and revision.

Distances measured in light-years; light travels at ~300,000 km/s

Scientific notation helps handle large/small numbers.  γ

Observing the Sky

Constellations = regions in the sky (88 official).

Sky appears to move due to Earth’s rotation (24h) and orbit (365 days).        

Zenith = overhead; meridian = N to S through zenith.

Ecliptic = Sun'... Continue reading "Fundamental Concepts in Astronomy and Astrophysics" »

Chapter 1: Electromagnetics Fundamentals

Gauss's Law

Gauss's Law for Electricity: The total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity ($\epsilon_0$).

Gauss's Law for Magnetism (Eq. 6.3): This integral is zero because magnetic field lines always form closed loops; magnetic monopoles do not exist.

Gauss's Law for Electricity (Eq. 6.1): This integral can be non-zero since positive and negative charges can be isolated, leading to the surface integral equaling $Q$, the enclosed charge.

Wave Characteristics

The velocity with which the envelope—or equivalently the wave group—travels through the medium is called the group velocity.

A traveling wave is characterized by a spatial wavelength ($\lambda$... Continue reading "Electromagnetics Principles and Transmission Line Fundamentals" »

Motion and Force Formulas

• Speed = Distance ÷ Time (Distance in m, Time in s)
• Acceleration = Change in velocity ÷ Time (Velocity in m/s, Time in s)
• Force = Mass × Acceleration (Mass in kg, Acceleration in m/s²)
• Weight = Mass × Gravitational field strength (g = 9.8 N/kg)

Density and Energy Equations

• Density = Mass ÷ Volume (Mass in kg, Volume in m³)
• Kinetic Energy (KE) = ½ × Mass × Speed² (Mass in kg, Speed in m/s)
• Gravitational Potential Energy (GPE) = Mass × g × Height (Mass in kg, Height in m)
• Work Done = Force × Distance (Force in N, Distance in m)
• Power = Energy transferred ÷ Time (Energy in J, Time in s)
• Efficiency = (Useful energy output ÷ Total energy input) × 100%

Waves, Electricity, and Pressure

• Wave speed = Frequency × Wavelength

Kirchhoff’s Current Law (KCL)

Statement:

At any junction (node) in an electrical circuit, the algebraic sum of currents is zero

∑ I=0

Explanation:

• At a junction, current cannot accumulate.

• Therefore, the total current entering must be equal to the total current leaving.

Example:
If currents I1I_1I1​ and I2I_2I2​ enter a node and I3I_3I3​ and I4I_4I4​ leave:     I1​+I2​=I3​+I4​  

2) Kirchhoff’s Voltage Law (KVL)

Statement:

In any closed loop of an electrical circuit, the algebraic sum of all voltages is zero.

∑V=0

Explanation:

• While moving around a closed loop, the sum of voltage rises equals the sum of voltage drops.

• This law is based on the conservation of energy.

Example:
For a loop with a source EEE and voltage drops V1​,V2​:... Continue reading "For an aeroplane hydraulic supply circuit, the correct statement is :" »

Polygon Rendering Methods Defined

• Polygon rendering methods are techniques used to calculate how 3D polygon surfaces appear when displayed on a 2D screen.
• They decide the distribution of light, color, and intensity on polygonal faces for realistic visualization.
• These methods control how smooth, bright, or sharp the surfaces look after illumination.
• They help convert geometric data into shaded, visible surfaces through lighting equations.
• These methods balance image quality and computational speed in computer graphics applications.

Types of Polygon Rendering Methods

Constant Intensity Shading (Flat Shading)

• Lighting is calculated once for the entire polygon, giving one uniform color.
• Produces a faceted appearance, where individual polygons are clearly

Methods of Charging

• Charging by friction: Involves one material losing electrons and the other gaining. This usually occurs when you rub two objects together and is determined by the triboelectric series.
• Charging by induction: The process where a charged particle is held near an uncharged particle.

Kirchhoff's Laws

1st Law: The current in equals the current out.

2nd Law: EMF equals the Potential Difference (P.D.) on a loop.

Electric Shock Severity

Factors that affect the severity of a shock:

• The amount of current (A) involved in the electric circuit
• Duration and time of exposure

Material Conductivity

Conductors: Allow electrons to pass readily through them (e.g., copper wire).

Insulators: Restrict the movement of charge (e.g., plastic sheath).

Semi-conductors:... Continue reading "Fundamental Principles of Electricity and Circuit Components" »

1. What is a Free Body Diagram (FBD)?

A Free Body Diagram (FBD) is a simple sketch that shows all the forces acting on an object. The object is usually represented as a dot or a simple shape, and arrows are used to show the direction and magnitude of each force. The purpose is to help analyze how forces affect the object's motion.

2. What is a Co-planar Concurrent Force System?

A co-planar concurrent force system is a set of forces that all lie in the same plane and meet at a single point. In this system, the forces act on the same object but are applied from different directions.

• Co-planar: Forces exist on the same flat surface.
• Concurrent: All force vectors intersect at one common point.

3. Equilibrium Equations for a Body in Space

The equilibrium... Continue reading "Essential Engineering Mechanics Principles and Formulas" »

1-D Motion

Can be described with zero displacement

Cannot be described with zero distance

Distance [x] = how far you move

Displacement [Δx] = distance from start to end

Speed = how fast [v = d/t]

Velocity = speed and direction [v = Δx/Δt]

Position/time: where we are at any given time

velocity = slope

v decreasing: A -> E

stationary: D

v increasing: A/none

greatest speed: A

Velocity/time: how fast we're going at any given time

acceleration/speeding up = slope

Stationary: A, L

Constant: H, E, D

Slowing down: K, J, I

Speeding up: B, C, F, G

Acceleration

Kinematic Equations:

1. V [end velocity] = V₀ [initial velocity] + at

ex. How fast do we hit the ground?

t = 20s

a = g = ~9.8 m/s²

x = 0m (x-axis intercept)

V₀... Continue reading "Essential Concepts in Classical Mechanics Physics" »

Critical Frequency (f_c) and MUF

Critical Frequency (f_c)

The maximum frequency at which a radio wave can be transmitted vertically and still be reflected back by the ionosphere.

Formula: f_c = 9√N_max

Where N_max is the maximum electron density (electrons/m³) in the ionosphere.

Maximum Usable Frequency (MUF)

The highest frequency that can be used for skywave communication between two given points, such that the wave is still reflected by the ionosphere.

Formula: MUF = f_c / cos(θ)

Where θ is the angle of incidence.

Virtual Height

The apparent height at which a radio wave appears to be reflected from the ionosphere, assuming it traveled in a straight line at the speed of light. In reality, the wave is refracted gradually, but the virtual height helps... Continue reading "Ionospheric Radio Propagation: Key Parameters and Principles" »

Introduction to Computational Fluid Dynamics (CFD)

Definition of CFD: CFD is the process of mathematically predicting physical fluid flow by solving the governing equations using computational power. Every CFD analysis uses a mathematical model and numerical method based on the Navier-Stokes (N-S) equations. Physical properties are calculated based on defined operating conditions.

Main objectives:

• Minimize the cost of the system
• Understanding and comprehension of the problem
• Improve behavior
• Reduce the time and cost of the design stage

3 Fundamental Principles:

1. Mass is conserved
2. F=m*a (Newton's 2nd Law)
3. Energy is conserved

Mass Conservation Principle: The rate of increase of mass in a fluid element equals the net rate of flow of mass into the fluid element.... Continue reading "CFD: Understanding Fluid Flow Through Computational Analysis" »