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

Uniformly Distributed Load (UDL) and Varying Load (UVL)

Converting Distributed Loads to Equivalent Point Loads

1. Uniformly Distributed Load (UDL)

Definition: A load that is evenly spread across a specific length ($L$) of a beam or structure.

Magnitude of Equivalent Point Load ($W$):

$$W = w \times L$$

• $w$: Intensity of UDL (N/m or kN/m)
• $L$: Length over which the UDL acts

The equivalent point load $W$ acts at the geometric center of the distributed load (at $L/2$ from either end).

UDL Diagram and Equivalent Point Load:

|‾‾‾‾‾‾‾‾‾‾|
| w N/m |
|___________|

Equivalent:

| | ↓ W = w × L
| | (at L/2)
|_______________

2. Uniformly Varying Load (UVL)

Definition: A load whose intensity varies linearly across the beam length, typically... Continue reading "Structural Loads and Support Reactions in Engineering Mechanics" »

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" »

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

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" »

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" »

Wave Properties and Characteristics

1. Mechanical waves can travel in any type of medium.

2. Refraction occurs when the amplitude of a wave changes as it goes from one medium to another.

Wave Classification and Behavior

• Transverse waves move particles back and forth along the same direction in which the waves travel.
• Mechanical waves can travel either through matter or through empty space.
• The amount of diffraction depends on the size of the obstacle and the wavelength of the wave.

Multiple Choice Questions

Which of the following is NOT a medium through which a mechanical wave can travel?

Answer: b. vacuum

Sound waves do not travel through a(n) _____.

Answer: d. empty space

Sound waves are _____.

Answer: a. longitudinal

Which of the following is transferred

DC Motor Speed-Torque Characteristics

• Graph Interpretation

  • Y-axis: Speed (N).
  • X-axis: Torque (T).
  • Shape: Linear downward slope (speed decreases as torque increases).

• Speed-Torque Formula

  N=V−IaRaϕN=ϕV−Ia​Ra​​,
  where I_a = armature current, R_a = armature resistance, ϕ = flux.

• Key Performance Points

  • At No Load: High speed, low torque.
  • At Full Load: Low speed, high torque (due to armature reaction).

• Applications

  Used in electric vehicles and cranes for variable speed control.

Working Principle of 3-Phase Induction Motor

• Stator Function

  • A 3-phase AC supply produces a Rotating Magnetic Field (RMF).
  • RMF Speed (Synchronous Speed, N_s): Ns=120fPNs​=P120f​.

• Rotor Operation

  • Conductors (aluminum bars) are cut by the RMF, inducing current (Faraday’s

Capillary Action and Surface Tension

Capillary action describes the phenomenon where the level of a liquid inside a narrow tube (relative to its container) is either raised or lowered. This height difference is maintained by surface tension forces. The direction and magnitude of this change depend on the liquid's surface tension and its interaction with the tube material (wettability).

The vertical component of the surface tension force acting on the tube walls must balance the weight of the liquid column of height h. Horizontal forces typically cancel out.

The capillary height h can be determined by balancing these forces:

• Surface tension force (vertical component): Fv = γ · 2πR · cosθ
• Weight of liquid column: P = ρ · g · πR2h

Equating... Continue reading "Fundamental Fluid Properties and Transport Phenomena" »

Santa Maria degli Angeli (Florence)

(Demolished after 3 years)

• Blended integration and relation of elements.
• Centralized floorplan: Representing an aesthetic ideal and an expression of the order of the universe – absolute symmetry.
• Surrounded by a world of well-proportioned beauty.
• Relation with Villa Rotonda; centralized building as a key urban form.

Michelozzo: Palazzo Medici (Florence)

• An urban palace where the facade is an important aspect.
• The wall treatment softens and smooths in the upper levels, representing the wealth of the Medici family.
• Exterior conveys solemnity, giving higher status to the city as well.
• Features a very heavy cornice at the top.

Leon Battista Alberti: Theory and Practice

• Had extensive contact with Florentine Humanists; friend