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

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" »

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

Thermal Expansion and Heat Energy Calculations

Section 4.1-2: Thermal Properties

The change in length due to thermal expansion is calculated using the following formula:

L₂ - L₁ = αL₁(T₂ - T₁)

• α (Alpha): Coefficient of thermal expansion, measured in °C^-1 or °F^-1.
• L₁ & L₂: Initial and final lengths, measured in mm (in), corresponding to temperatures T₁ & T₂.

Heat Energy Required for Temperature Change

The amount of heat energy ($H$) required to change the temperature of a material is given by:

H = C W (T₂ - T₁)

• H: Amount of heat energy, measured in J (Btu).
• C: Specific heat of the material, measured in J/Kg°C (Btu/lb°F).
• W: Weight of the material, measured in kg (lb).
• (T₂ - T₁): Change in temperature, measured in °C (°F).

Volumetric Specific

Numerical Methods for Solving Equations

1.1 Solving an Algebraic System

This code defines a function f(V) and then solves the system f([x,y,z]) = [x,y,z] to find its fixed points using the algsys command.

faux(x,y,z) := [(x^2)/2 + 1/3, x+y+z/4, x^2-y^2+(z^2)/4];
f(V) := faux(V[1], V[2], V[3]);

ecus : f([x,y,z]) - [x,y,z];
algsys(ecus, [x,y,z]), numer;

1.2 Fixed-Point Iteration Method

This block implements the fixed-point iteration method. It starts with an initial guess (seed) and iteratively applies the function f until the norm of the difference between successive iterations is smaller than a given tolerance (10^-14).

nor(V) := sqrt(V.V);
fpprec:100;

block(
  semilla:[0,0,0],
  while nor(f(semilla)-semilla) > 10^(-14) do 
    semilla:bfloat(

Mamíferos: Las hembras tienen mamas que producen leche para alimentar a las crías, el cuerpo está cubierto por pelos. La función principal es proteger del frio al animal.
Pelaje: raíz dentro del funículo piloso .Los pelos nuevos sacan los pelos viejos. La glándula sebácea lo hace más flexible el pelo. Lana (largo y fino), cerda (áspero y grueso), vello (suave y corto) y púa (largo y puntiagudo)
La temperatura: Es constante. Si sube o baja la temperatura siempre se mantiene constante.
Hibernación: desciende -10 Cº / Duerme no come y se esconde.
Invernación: baja la temperatura pero un duerme profundamente, come y hace algunas actividades.
La fecundación interna se produce en el ovulo con el esperma.
Sistema digestivo: Boca -faringe-

A/C/B/D/A/B/B/B/B/C/A/B/A/D/A/C/C/C/A/B/D/A/A/B/B/A/C/D/B/D

1. Stopwatch Accuracy

a) Stopwatch

b) To have more accuracy

c) i) 3rd

ii) (3.93 + 4.07 + 3.99) / 3 = 11.99 / 3 = 4

iii) 4 / 10 = 0.40

2. Water Speed Measurement

a) First, measure the distance between bridge X and bridge Y. Then, place the stick in the water at bridge X and time how long it takes to reach bridge Y. Calculate the speed by dividing the distance by the time. Repeat this process at least three times. Add all the results together and divide by three to get the average speed.

b) 2nd box

3. Acceleration and Force

a) i) 24 / 60 = 0.4 m/s²

ii) 7.5 × 10⁵ × 0.4 = 300,000 N

b) Speeding up / Slowing down / Steady speed / At rest

4. Resultant Force and Density

a) i) 280 - 250 = 30 N

ii) Up

b)... Continue reading "Physics Exam Answers and Explanations" »

Energy: Units and Types

• Unit of energy: Joule (J)
• Conservation of Energy: Energy cannot be created or destroyed, only transferred or transformed.
• Kinetic Energy: Energy of motion.
• Potential Energy: Stored due to position (e.g., at the top of a pendulum).

Conduction

• Occurs mainly in solids.
• Particles transfer energy by vibrating and passing it to neighbors.
• Metals are good conductors.
• Poor conductors (insulators), e.g., air and layers of clothing.

Convection

• Happens only in fluids (liquids and gases).
• Heated fluid becomes less dense → rises.
• Cooler fluid becomes more dense → sinks.
• Creates convection currents.
• Example: Hot water in a pan rises to the top.

Radiation

• Transfer by infra-red waves.
• Only method that works in a vacuum (space).
• Best absorber/emitter: