From 6177c5477002873baf097bea2df13af1b5663e85 Mon Sep 17 00:00:00 2001
From: pauld0051 <62159791+pauld0051@users.noreply.github.com>
Date: Sun, 21 Jan 2024 18:27:43 +0100
Subject: [PATCH] Add new styling, update bootstrap, general update
---
header.html | 26 +-
latex.html | 6 +-
latex_insert.html | 34 ++
physics_A1_kinematics.html | 249 +++++------
physics_A2_forces_and_momentum.html | 394 +++++++++---------
physics_A3_work_energy_power.html | 326 +++++++--------
physics_A4_rigid_body_mechanics.html | 393 ++++++++---------
physics_A5_special_relativity.html | 356 +++++++++-------
physics_B1_thermal_energy.html | 289 +++++++------
physics_B2_greenhouse_effect.html | 131 +++---
physics_B3_gas_laws.html | 202 +++++----
physics_B4_thermodynamics.html | 261 ++++++------
physics_B5_current_circuits.html | 265 ++++++------
physics_C1_simple_harmonic_motion.html | 357 +++++++---------
physics_C2_wave_model.html | 161 +++----
physics_C3_wave_phenomena.html | 352 +++++++++-------
physics_C5_doppler_effect.html | 216 +++++-----
physics_D1_gravitational_fields.html | 295 +++++++++++++
physics_D2_electric_magnetic_fields.html | 278 ++++++++++++
physics_D3_motion_electromagnetic_fields.html | 164 ++++++++
physics_D4_induction.html | 164 ++++++++
physics_E1_structure_atom.html | 164 ++++++++
physics_E2_quantum_physics.html | 164 ++++++++
physics_E3_radioactive_decay.html | 164 ++++++++
physics_E5_fusion_stars.html | 164 ++++++++
physics_mathematical_equations.html | 2 +-
scripts/main.js | 2 +
scripts/symbolsLatex.js | 67 ++-
style/base.css | 11 +
style/symbols.css | 9 +-
style/symbols_physics.css | 249 +++++++++++
31 files changed, 3950 insertions(+), 1965 deletions(-)
create mode 100644 latex_insert.html
create mode 100644 physics_D1_gravitational_fields.html
create mode 100644 physics_D2_electric_magnetic_fields.html
create mode 100644 physics_D3_motion_electromagnetic_fields.html
create mode 100644 physics_D4_induction.html
create mode 100644 physics_E1_structure_atom.html
create mode 100644 physics_E2_quantum_physics.html
create mode 100644 physics_E3_radioactive_decay.html
create mode 100644 physics_E5_fusion_stars.html
create mode 100644 style/symbols_physics.css
diff --git a/header.html b/header.html
index 375067a..16a5098 100644
--- a/header.html
+++ b/header.html
@@ -15,7 +15,7 @@
@@ -99,6 +99,28 @@
C5 Doppler Effect
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+
+
+
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+
diff --git a/latex.html b/latex.html
index ffaf067..070c277 100644
--- a/latex.html
+++ b/latex.html
@@ -47,6 +47,7 @@ Copy Kinematic Equations
Make your own LaTeX
+
@@ -80,9 +81,8 @@
Make your own LaTeX
-
-
-
+
+
diff --git a/latex_insert.html b/latex_insert.html
new file mode 100644
index 0000000..5e2280f
--- /dev/null
+++ b/latex_insert.html
@@ -0,0 +1,34 @@
+
+ Make your own LaTeX
+
+
+
+
+
+
+
+ Transparent
+ White
+
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+
+
+ Small
+ Normal
+ Large
+ Very Large
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+ Render PNG
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diff --git a/physics_A1_kinematics.html b/physics_A1_kinematics.html
index 1af5f05..341a8d5 100644
--- a/physics_A1_kinematics.html
+++ b/physics_A1_kinematics.html
@@ -15,7 +15,7 @@
-
+
@@ -40,144 +40,147 @@
Copy Kinematic Equations
-
- Click the LaTeX buttons to copy LaTeX code for use in your projects or paste into the LaTeX PNG generator below. For
- instant use in documents or on social media, or you can copy the basic formatted equations.
-
-
- Note: The LaTeX PNG generator may not display images correctly in Firefox. For the best experience, please use
- Chrome or Edge browsers.
-
-
-
-
-
+
+ Click the LaTeX buttons to copy LaTeX code for use in your projects or paste into the LaTeX PNG generator below. For
+ instant use in documents or on social media, or you can copy the basic formatted equations.
+
+
+ Note: The LaTeX PNG generator may not display images correctly in Firefox. For the best experience, please use
+ Chrome or Edge browsers.
+
+
+
+ How to Use
+
+
-
-
-
A.1 Kinematic Equations - LaTeX
-
-
-
-
- \( s = \frac{u + v}{2} \cdot t \)
-
-
Copied!
-
-
s = \frac{u + v}{2} \cdot t
+
+ A.1 Kinematic Equations - LaTeX
+
+
+
+
+ \( s = \frac{u + v}{2} \cdot t \)
-
-
-
-
- \( v = u + at \)
-
-
Copied!
-
-
v = u + at
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( v = u + at \)
-
-
-
-
- \( s = ut + \frac{1}{2}at^2 \)
-
-
Copied!
-
-
s = ut + \frac{1}{2}at^2
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( s = ut + \frac{1}{2}at^2 \)
-
-
-
-
- \( v^2 = u^2 + 2as \)
-
-
Copied!
-
-
v^2 = u^2 + 2as
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( v^2 = u^2 + 2as \)
-
-
-
- A.1 Kinematic Equations - Basic
-
-
-
-
-
- s = (u + v)/2 × t
-
-
Copied!
-
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ A.1 Kinematic Equations - Basic
+
+
+
+
+ s = (u + v)/2 × t
-
-
-
-
- v = u + at
-
-
Copied!
-
+
+ Copy Text
+
+
Copied!
+
+
+
+
+ v = u + at
-
-
-
-
- s = ut + 1/2 at²
-
-
Copied!
-
+
+ Copy Text
+
+
Copied!
+
+
+
+
+ s = ut + 1/2 at²
-
-
-
-
- v² = u² + 2as
-
-
Copied!
-
+
+ Copy Text
+
+
Copied!
+
+
+
+
+ v² = u² + 2as
-
+
+ Copy Text
+
+
Copied!
+
+
+
Make your own LaTeX
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-
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- Transparent
- White
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- Small
- Normal
- Large
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diff --git a/physics_A2_forces_and_momentum.html b/physics_A2_forces_and_momentum.html
index 304202d..6cc0d0d 100644
--- a/physics_A2_forces_and_momentum.html
+++ b/physics_A2_forces_and_momentum.html
@@ -15,7 +15,7 @@
-
+
@@ -56,246 +56,226 @@
Copy Force and Momentum Equations
A.2 Force and Momentum Equations - LaTeX
-
-
-
- \( F_{f} \leq \mu_{s} F_{N} \)
-
+
+
+
+
+ \( F_{f} \leq \mu_{s} F_{N} \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( F_{f} = \mu_{k} F_{N} \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( F_{H} = -kx \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( F_{d} = 6\pi\eta rv \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( F_{b} = \rho Vg \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( F_{g} = mg \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( p = mv \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( J = F\Delta t \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( F = ma = \frac{\Delta p}{\Delta t} \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( a = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2} \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( v = \frac{2\pi r}{T} = \omega r \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+
+ A.2 Force and Momentum - Basic
+
+
+
+
Fₑ ≤ μₛFₙ
+
Copy Text
Copied!
-
F_{f} \leq \mu_{s} F_{N}
-
-
-
-
- \( F_{f} = \mu_{k} F_{N} \)
-
+
+
+
Fₑ = μₖFₙ
+
Copy Text
Copied!
-
F_{f} = \mu_{k} F_{N}
-
-
-
-
- \( F_{H} = -kx \)
-
+
+
+
Fₕ = -kx
+
Copy Text
Copied!
-
F_{H} = -kx
-
-
-
- \( F_{d} = 6\pi\eta rv \)
-
+
+
Fd = 6πηrv
+
Copy Text
Copied!
-
F_{d} = 6\pi\eta rv
-
-
-
- \( F_{b} = \rho Vg \)
-
+
+
Fb = ρVg
+
Copy Text
Copied!
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F_{b} = \rho Vg
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-
-
- \( F_{g} = mg \)
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+
+
Fg = mg
+
Copy Text
Copied!
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F_{g} = mg
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-
-
- \( p = mv \)
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+
p = mv
+
Copy Text
Copied!
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p = mv
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-
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- \( J = F\Delta t \)
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+
+
J = FΔt
+
Copy Text
Copied!
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J = F\Delta t
-
-
-
- \( F = ma = \frac{\Delta p}{\Delta t} \)
-
+
+
F = ma = Δp/Δt
+
Copy Text
Copied!
-
F = ma = \frac{\Delta p}{\Delta t}
-
-
-
- \( a = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2} \)
-
+
+
a = v²/r = ω²r = 4π²r/T²
+
Copy Text
Copied!
-
a = \frac{v^2}{r} = \omega^2 r = \frac{4\pi^2 r}{T^2}
-
-
-
- \( v = \frac{2\pi r}{T} = \omega r \)
-
+
+
v = 2πr/T = ωr
+
Copy Text
Copied!
-
v = \frac{2\pi r}{T} = \omega r
-
-
- A.2 Force and Momentum - Basic
-
-
-
-
- Fₑ ≤ μₛFₙ
-
-
Copied!
-
Static Friction Equation
-
-
-
-
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- Fₑ = μₖFₙ
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Copied!
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Kinetic Friction Equation
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-
-
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- Fₕ = -kx
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Hooke's Law Equation
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-
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- Fd = 6πηrv
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Drag Force Equation
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-
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- Fb = ρVg
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Copied!
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Buoyant Force Equation
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-
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- Fg = mg
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Gravitational Force Equation
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- p = mv
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Momentum Equation
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- J = FΔt
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Impulse Equation
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-
-
-
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- F = ma = Δp/Δt
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Copied!
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Newton's Second Law Equation
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+
+
-
-
-
- a = v²/r = ω²r = 4π²r/T²
-
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Copied!
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Circular Motion Acceleration Equation
+
+ Make your own LaTeX
+
+
+
+
+
+
+
+ Transparent
+ White
+
-
-
-
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- v = 2πr/T = ωr
-
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Copied!
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Circular Motion Velocity Equation
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+
+
+ Small
+ Normal
+ Large
+ Very Large
+ Huge
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- Make your own LaTeX
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+
@@ -55,176 +55,166 @@ Copy Work, Energy and Power Equations
Note: Some limitations exist in the basic form, as subscripts are not always available.
-
- A.3 Work, Energy and Power Equations - LaTeX
-
-
-
- \( W = Fs\cos\theta \)
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W = Fs\cos\theta
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-
-
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- \( E_k = \frac{1}{2}mv^2 = \frac{p^2}{2m} \)
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E_k = \frac{1}{2}mv^2 = \frac{p^2}{2m}
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-
-
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- \( \Delta E_p = mg\Delta h \)
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\Delta E_p = mg\Delta h
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-
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- \( E_H = \frac{1}{2} k \Delta x^2 \)
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E_H = \frac{1}{2} k \Delta x^2
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- \( P = \frac{\Delta W}{\Delta t} \)
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P = \frac{\Delta W}{\Delta t}
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- \( P = Fv \)
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P = Fv
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- \( \eta = \frac{E_{\text{output}}}{E_{\text{input}}} = \frac{P_{\text{output}}}{P_{\text{input}}} \)
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\eta = \frac{E_{\text{output}}}{E_{\text{input}}} = \frac{P_{\text{output}}}{P_{\text{input}}}
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- A.3 Work, Energy and Power - Basic
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-
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- W = F • s • cos(θ)
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Work
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- Eₖ = ½mv² = p²/2m
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Kinetic Energy
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- ΔEₚ = mgΔh
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Potential Energy
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- Eₕ = ½kΔx²
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Elastic Potential Energy
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- P = ΔW/Δt
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Power
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- P = Fv
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Power
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- η = Eₒᵤₜₚᵤₜ/Eᵢₙₚᵤₜ = Pₒᵤₜₚᵤₜ/Pᵢₙₚᵤₜ
-
-
Copied!
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Efficiency
-
-
-
-
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- Make your own LaTeX
-
+
+ A.3 Work, Energy and Power Equations - LaTeX
+
+
+
+
+ \( W = Fs\cos\theta \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( E_k = \frac{1}{2}mv^2 = \frac{p^2}{2m} \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( \Delta E_p = mg\Delta h \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+ \( E_H = \frac{1}{2} k \Delta x^2 \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
+ \( P = \frac{\Delta W}{\Delta t} \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
+ \( P = Fv \)
+
+
+ Copy LaTeX
+
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Copied!
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+
+
+
+ \( \eta = \frac{E_{\text{output}}}{E_{\text{input}}} = \frac{P_{\text{output}}}{P_{\text{input}}} \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
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- Transparent
- White
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+ A.3 Work, Energy and Power - Basic
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+
+
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W = F • s • cos(θ)
+
Copy Text
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Copied!
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+
+
+
Eₖ = ½mv² = p²/2m
+
Copy Text
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Copied!
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+
+
+
ΔEₚ = mgΔh
+
Copy Text
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Copied!
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+
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Eₕ = ½kΔx²
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Copy Text
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Copied!
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+
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P = ΔW/Δt
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Copy Text
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Copied!
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+
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P = Fv
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Copy Text
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Copied!
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η = Eₒᵤₜₚᵤₜ/Eᵢₙₚᵤₜ = Pₒᵤₜₚᵤₜ/Pᵢₙₚᵤₜ
+
Copy
+ Text
+
Copied!
+
+
+
-
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- Small
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- Large
- Very Large
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+ Make your own LaTeX
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+ Transparent
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@@ -56,243 +56,258 @@ Copy Rigid Body Mechanics Equations
A.3 Work, Energy and Power Equations - LaTeX
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- \( \tau = Fr\sin(\theta) \)
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\tau = Fr\sin(\theta)
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- \( \Delta \theta = \frac{\omega_i + \omega_f}{2}t \)
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\Delta \theta = \frac{\omega_i + \omega_f}{2}
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- \( \omega_f = \omega_i + \alpha t \)
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\omega_f = \omega_i + \alpha t
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- \( \Delta\theta = \omega_{i}t + \frac{1}{2}at^2 \)
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\Delta\theta = \omega_{i}t + \frac{1}{2}at^2
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- \( \omega_{f}^2 = \omega_{i}^2 + 2a\Delta\theta \)
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\omega_{f}^2 = \omega_{i}^2 + 2a\Delta\theta
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- \( I = \Sigma mr^2 \)
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I = \Sigma mr^2
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- \( \tau = I\alpha \)
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\tau = I\alpha
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- \( L = I\omega \)
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L = I\omega
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- \( \Delta L = \tau \Delta t \)
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\Delta L = \tau \Delta t
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- \( \Delta L = \Delta (I\omega) \)
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\Delta L = \Delta (I\omega)
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- \( E_k = \frac{1}{2}I\omega^2 = \frac{L^2}{2I} \)
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Copied!
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E_k = \frac{1}{2}I\omega^2 = \frac{L^2}{2I}
+
+
+
+
+ \( \tau = Fr\sin(\theta) \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
+
+ \( \Delta \theta = \frac{\omega_i + \omega_f}{2}t \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
+
+ \( \omega_f = \omega_i + \alpha t \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
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+ \( \Delta\theta = \omega_{i}t + \frac{1}{2}at^2 \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
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+ \( \omega_{f}^2 = \omega_{i}^2 + 2a\Delta\theta \)
+
+
+ Copy LaTeX
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Copied!
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+
+
+
+
+ \( I = \Sigma mr^2 \)
+
+
+ Copy LaTeX
+
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Copied!
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+
+
+
+
+ \( \tau = I\alpha \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
+
+ \( L = I\omega \)
+
+
+ Copy LaTeX
+
+
Copied!
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+
+
+
+
+ \( \Delta L = \tau \Delta t \)
+
+
+ Copy LaTeX
+
+
Copied!
+
+
+
+
+
+ \( \Delta L = \Delta (I\omega) \)
+
+
+ Copy LaTeX
+
+
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+ \( E_k = \frac{1}{2}I\omega^2 = \frac{L^2}{2I} \)
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- A.4 Rigid Body Mechanics - Basic
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- τ = Fr sin θ
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τ = Fr sin θ
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Torque
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Δθ = (ωᵢ + ωf) / 2 • t
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Angular Displacement
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- ωf = ωᵢ + αt
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ωf = ωᵢ + αt
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Angular Velocity
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- Δθ = ωi t + ½ at²
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Δθ = ωᵢ t + ½ at²
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Angular Displacement
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- ωf ² = ωi ² + 2aΔθ
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Angular Velocity
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- I = Σmr²
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I = Σmr²
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Moment of Inertia
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- τ = Iα
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τ = Iα
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- L = Iω
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L = Iω
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L = Iω
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- ΔL = τΔt
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+
ΔL = τΔt
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ΔL = τΔt
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- ΔL = Δ(Iω)
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ΔL = Δ(Iω)
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- Ek = ½Iω² = L²/2I
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@@ -54,231 +54,271 @@ Copy Galilean and Special Relativity Equations
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x' = \gamma (x - vt) where \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}
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t' = \gamma ( t - \frac{v x}{c^2} )
+
+
+
+ \( t' = \gamma \left( t - \frac{v x}{c^2} \right) \)
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u' = \frac{u - v}{1 - \frac{u v}{c^2}}
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(\Delta s)^2 = (c \Delta t)^2 - \Delta x^2
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- \( \Delta t = \gamma \Delta t_0 \)
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\Delta t = \gamma \Delta t_0
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+
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+ \( (\Delta s)^2 = (c \Delta t)^2 - \Delta x^2 \)
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L = \frac{L_0}{\gamma}
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\tan(\theta) = \frac{v}{c}
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+ \( \tan(\theta) = \frac{v}{c} \)
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- A.5 Galilean and Special Relativity - Basic
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x' = x - vt
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Lorentz Transformation for Position
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t' = γ(t - vx/c²)
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u' = (u - v)/(1 - uv/c²)
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(Δs)² = (cΔt)² - Δx²
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@@ -15,7 +15,7 @@
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@@ -56,169 +56,202 @@ Copy Thermal Energy Transfer Equations
B.1 Thermal Energy Transfers Equations - LaTeX
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-
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- \( \rho = \frac{m}{V} \)
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- \( \overline{E}_k = \frac{3}{2}k_B T \)
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\overline{E}_k = \frac{3}{2}k_B T
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+
+ \( \overline{E}_k = \frac{3}{2}k_B T \)
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- \( Q = mc\Delta T \)
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- \( \frac{\Delta Q}{\Delta t} = kA \frac{\Delta T}{\Delta x} \)
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\frac{\Delta Q}{\Delta t} = kA \frac{\Delta T}{\Delta x}
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-
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- \( L = \sigma A T^4 \)
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+
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- \( \lambda_{\text{max}} T = 2.9 \times 10^{-3} \text{ mK} \)
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\lambda_{\text{max}} T = 2.9 \times 10^{-3} \text{ mK}
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+
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B.1 Thermal Energy Transfers - Basic
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Density
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ρ = m/V
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- E̅k = 3/2 kBT
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E̅k = 3/2 kBT
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- Q = mcΔT
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Heat Transfer (Specific Heat Capacity)
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Q = mcΔT
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- ΔQ/Δt = kA ΔT/Δx
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ΔQ/Δt = kA ΔT/Δx
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- L = σ A T⁴
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- b = L/4πd²
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Luminosity
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b = L/4πd²
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- λmax T = 2.9 × 10⁻³ mK
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λmax T = 2.9 × 10⁻³ mK
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@@ -54,86 +54,95 @@ Copy Greenhouse Effect Equations
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emissivity = \frac{power radiated per unit area}{\sigma T^4}
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+ B.2 Greenhouse Effect Equations - LaTeX
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+
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+ \( \text{emissivity} = \frac{\text{power radiated per unit area}}{\sigma T^4} \)
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albedo = \frac{total scattered power}{total incident power}
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+ \( \text{albedo} = \frac{\text{total scattered power}}{\text{total incident power}} \)
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emissivity = power radiated per unit area / σT⁴
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diff --git a/physics_B3_gas_laws.html b/physics_B3_gas_laws.html
index e53fe59..12f0d87 100644
--- a/physics_B3_gas_laws.html
+++ b/physics_B3_gas_laws.html
@@ -15,7 +15,7 @@
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+
@@ -46,142 +46,140 @@
Copy Gas Laws Equations
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\frac{PV}{T} = \text{constant}
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- \( PV = nRT = Nk_B T \)
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PV = nRT = Nk_B T
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+ \( PV = nRT = Nk_B T \)
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P = F / A
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- PV / T = constant
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PV / T = constant
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PV = nRT = NkᵦT
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Ideal Gas Law
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Kinetic Theory of Gases
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+ content="Find a curated list of essential Physics Thermodynamics Equations tailored for the IB curriculum at Pangram World. Effortlessly access and copy equations in LaTeX, or basic form, ideal for students and educators in the field of physics." />
Physics Greenhouse Effect Equations | Pangram World
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+ \( \Delta U = \frac{3}{2}nR\Delta T = \frac{3}{2}Nk_B\Delta T \)
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+ \( \eta = \frac{\text{useful work}}{\text{input energy}} \)
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+
-
- B.4 Thermodynamics Equations - Basic
+
+ B.4 Thermodynamics Equations - Basic
+
-
-
- Q = ΔU + W
-
+
+
Q = ΔU + W
+
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-
First Law of Thermodynamics
-
-
-
- W = PΔV
-
+
+
W = PΔV
+
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-
Work Done by/on Gas
-
-
-
- ΔU = (³⁄₂)nRΔT = (³⁄₂)NkᵦΔT
-
+
+
ΔU = (³⁄₂)nRΔT = (³⁄₂)NkᵦΔT
+
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-
Change in Internal Energy
-
-
-
- ΔS = ΔQ/T
-
+
+
ΔS = ΔQ/T
+
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-
Entropy Change
-
-
-
- S = kᵦ ln Ω
-
+
+
S = kᵦ ln Ω
+
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-
Entropy Definition
-
-
-
- PV⁽⁵⁄³⁾ = constant
-
+
+
PV⁽⁵⁄³⁾ = constant
+
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-
Adiabatic Process for Monoatomic Ideal Gas
-
-
-
- η = useful work/input energy
-
+
+
η = useful work/input energy
+
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-
Efficiency of an Engine
-
-
-
- ηCarnot = 1 - Tc/Th
-
+
+
ηCarnot = 1 - Tc/Th
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Carnot Efficiency
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+
+
-
- Make your own LaTeX
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+ content="Find a curated list of essential Physics Current and Circuit Equations tailored for the IB curriculum at Pangram World. Effortlessly access and copy equations in LaTeX, or basic form, ideal for students and educators in the field of physics." />
Physics Current and Circuit Equations | Pangram World
@@ -15,7 +15,7 @@
-
+
@@ -39,241 +39,244 @@
- Copy Current and Circuit Equations
+ Copy Thermodynamics Equations
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-
- B.5 Current and Circuits Equations - LaTeX
+
+ B.5 Current and Circuits Equations - LaTeX
+
-
-
+
+
\( I = \frac{\Delta q}{\Delta t} \)
+
+
+ Copy LaTeX
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I = \frac{\Delta q}{\Delta t}
-
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+
+
\( V = \frac{W}{q} \)
+
+
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V = \frac{W}{q}
-
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+
+
\( R = \frac{V}{I} \)
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+
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R = \frac{V}{I}
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+
\( \rho = \frac{RA}{L} \)
+
+
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\rho = \frac{RA}{L}
-
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+
\( P = IV = I^2R = \frac{V^2}{R} \)
+
+
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P = IV = I^2R = \frac{V^2}{R}
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Series Circuits
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+
+
\( I = I_1 = I_2 = \dots \)
+
+
+ Copy LaTeX
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I = I_1 = I_2 = \dots
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\( V = V_1 + V_2 + \dots \)
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+
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V = V_1 + V_2 + \dots
-
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+
+
\( R_s = R_1 + R_2 + \dots \)
+
+
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R_s = R_1 + R_2 + \dots
-
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+
+
\( \varepsilon = I(R + r) \)
+
+
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\varepsilon = I(R + r)
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+
Parallel Circuits
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-
+
+
\( I = I_1 + I_2 + \dots \)
+
+
+ Copy LaTeX
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I = I_1 + I_2 + \dots
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\( V = V_1 = V_2 = \dots \)
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V = V_1 = V_2 = \dots
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\( \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \)
+
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\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \dots
-
+
+
-
- B.5 Current and Circuits - Basic
+
+ B.5 Current and Circuits - Basic
+
-
-
- I = Δq/Δt
-
+
+
I = Δq/Δt
+
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Current
-
+
-
-
- V = W/q
-
+
+
V = W/q
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Voltage
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+
-
-
- R = V/I
-
+
+
R = V/I
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Resistance
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+
-
-
- ρ = RA/L
-
+
+
ρ = RA/L
+
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Resistivity
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+
-
-
- P = IV = I²R = V²/R
-
+
+
P = IV = I²R = V²/R
+
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Power
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Series Circuits
-
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- I = I₁ = I₂ = ...
-
+
+
I = I₁ = I₂ = ...
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Current in Series
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- V = V₁ + V₂ + ...
-
+
+
V = V₁ + V₂ + ...
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Voltage in Series
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- Rₛ = R₁ + R₂ + ...
-
+
+
Rₛ = R₁ + R₂ + ...
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Total Resistance in Series
-
-
- ε = I(R + r)
-
+
+
ε = I(R + r)
+
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-
EMF in Series
-
+
Parallel Circuits
-
-
- I = I₁ + I₂ + ...
-
+
+
I = I₁ + I₂ + ...
+
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Current in Parallel
-
-
- V = V₁ = V₂ = ...
-
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V = V₁ = V₂ = ...
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-
Voltage in Parallel
-
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- 1/Rₚ = 1/R₁ + 1/R₂ + ...
-
+
+
1/Rₚ = 1/R₁ + 1/R₂ + ...
+
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Total Resistance in Parallel
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+ content="Find a curated list of essential Physics Simple Harmonic Motion Equations tailored for the IB curriculum at Pangram World. Effortlessly access and copy equations in LaTeX, or basic form, ideal for students and educators in the field of physics." />
Physics Simple Harmonic Motion Equations | Pangram World
@@ -15,7 +15,7 @@
-
+
@@ -41,248 +41,193 @@
Copy Simple Harmonic Motion Equations
- Click the LaTeX buttons to copy LaTeX code for use in your projects or paste into the LaTeX PNG generator
- below. For
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- C.1 Simple Harmonic Motion Equations - LaTeX
+
+ C.1 Simple Harmonic Motion Equations - LaTeX
+
-
-
+
+
\( a = -\omega^2 x \)
+
+
+ Copy LaTeX
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a = -\omega^2 x
-
+
-
-
+
+
\( T = \frac{1}{f} = \frac{2\pi}{\omega} \)
+
+
+ Copy LaTeX
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T = \frac{1}{f} = \frac{2\pi}{\omega}
-
-
-
-
- \( \omega = 2 \pi f \)
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\omega = 2 \pi f
-
+
-
-
- \( T = 2\pi\sqrt{\frac{m}{k}} \)
+
+
+ \( \omega = 2 \pi f \)
+
+
+ Copy LaTeX
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T = 2\pi\sqrt{\frac{m}{k}}
-
+
-
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- \( T = 2\pi\sqrt{\frac{l}{g}} \)
+
+
+ \( T = 2\pi\sqrt{\frac{m}{k}} \)
+
+
+ Copy LaTeX
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-
T = 2\pi\sqrt{\frac{l}{g}}
-
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- C.1 Simple Harmonic Motion - Additional High Level Content - LaTeX
+
-
-
- \( x = x_0 \sin(\omega t + \phi) \)
-
-
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x = x_0 \sin(\omega t + \phi)
-
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-
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- \( v = \omega x_0 \cos(\omega t + \phi) \)
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v = \omega x_0 \cos(\omega t + \phi)
-
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- \( v = \pm\omega\sqrt{x_0^2 - x^2} \)
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v = \pm\omega\sqrt{x_0^2 - x^2}
-
-
-
-
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- \( E_T = \frac{1}{2}m\omega^2 x_0^2 \)
-
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E_T = \frac{1}{2}m\omega^2 x_0^2
-
-
-
-
-
- \( E_p = \frac{1}{2}m\omega^2 x^2 \)
+
+
+ \( T = 2\pi\sqrt{\frac{l}{g}} \)
+
+
+ Copy LaTeX
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E_p = \frac{1}{2}m\omega^2 x^2
-
-
-
- C.1 Simple Harmonic Motion Equations - Basic
-
-
-
- a = -ω² x
-
-
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Acceleration
-
-
-
-
-
- T = 1/f = 2π/ω
-
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Period
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-
-
-
- ω = 2πf
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Angular Frequency
-
-
-
-
-
- T = 2π√(m/k)
-
-
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Period (Mass-Spring System)
-
-
-
-
-
- T = 2π√(l/g)
-
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Period (Pendulum)
+
+
+ C.1 Simple Harmonic Motion Equations - Basic
+
+
+
+
a = -ω² x
+
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+
+
+
+
T = 1/f = 2π/ω
+
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+
+
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+
ω = 2πf
+
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+
+
+
+
T = 2π√(m/k)
+
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+
+
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+
T = 2π√(l/g)
+
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+
+
-
- C.1 Simple Harmonic Motion - Additional High Level Content - Basic
-
-
-
- x = x₀ sin(ωt + φ)
-
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Displacement
-
-
-
-
-
- v = ωx₀ cos(ωt + φ)
-
-
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Velocity
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-
-
-
-
- v = ±ω√(x₀² - x²)
-
-
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Velocity at Position x
-
-
-
-
-
- Eₜ = ½ mω² x₀²
-
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Total Energy
-
-
-
-
-
- Eₚ = ½ mω² x²
-
-
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Potential Energy
-
-
+
+ C.1 Simple Harmonic Motion - Additional High Level Content - Basic
+
+
+
+
x = x₀ sin(ωt + φ)
+
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v = ωx₀ cos(ωt + φ)
+
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- Transparent
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v = ±ω√(x₀² - x²)
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Eₜ = ½ mω² x₀²
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-
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+
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Eₚ = ½ mω² x²
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Physics Wave Model Equations | Pangram World
@@ -15,7 +15,7 @@
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+
@@ -38,84 +38,91 @@
-
- Copy Wave Model Equations
-
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- C.2 Wave Model Equations - LaTeX
-
-
- \( v = f \lambda = \frac{\lambda}{T} \)
-
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v = f \lambda = \frac{\lambda}{T}
-
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-
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- C.2 Wave Model Equations - Basic
-
-
- v = fλ = λ/T
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Wave Velocity
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+
+ Copy Wave Model Equations
+
+ Click the LaTeX buttons to copy LaTeX code for use in your projects or paste into the LaTeX PNG generator
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+
+
+ \( v = f \lambda = \frac{\lambda}{T} \)
+
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+
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-
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+
+ C.2 Wave Model Equations - Basic
+
+
+
+ v = fλ = λ/T
+
+
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+ content="Find a curated list of essential Physics Wave Phenomena Equations tailored for the IB curriculum at Pangram World. Effortlessly access and copy equations in LaTeX, or basic form, ideal for students and educators in the field of physics." />
Physics Wave Phenomena Equations | Pangram World
@@ -15,7 +15,7 @@
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+
@@ -39,181 +39,211 @@
- Copy Wave Phenomena Equations
-
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- C.3 Wave Phenomena Equations - LaTeX
-
-
-
- \( \frac{n_1}{n_2} = \frac{\sin \theta_2}{\sin \theta_1} = \frac{v_2}{v_1} \)
-
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\frac{n_1}{n_2} = \frac{\sin \theta_2}{\sin \theta_1} = \frac{v_2}{v_1}
+
Copy Wave Phenomena Equations
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+ C.3 Wave Phenomena Equations - LaTeX
+
+
+
+
+ \( \frac{n_1}{n_2} = \frac{\sin \theta_2}{\sin \theta_1} = \frac{v_2}{v_1} \)
-
-
-
-
- \( \begin{align*} &\text{Constructive interference:} \\ &\text{path difference} = n\lambda \end{align*} \)
-
-
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-
\begin{align*} &\text{Constructive interference:} \\ &\text{path difference} = n\lambda
- \end{align*}
+
+ Copy LaTeX
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+
+
+
+
+ \( s = \frac{\lambda D}{d} \)
-
-
-
-
- \( \begin{align*} &\text{Destructive interference:} \\ &\text{path difference} = (n + \frac{1}{2})\lambda
- \end{align*} \)
-
-
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\begin{align*} &\text{Destructive interference:} \\ &\text{path difference} = (n + \frac{1}{2})\lambda
- \end{align*}
+
+ Copy LaTeX
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+
+
+
+
+ \begin{align*}
+ \text{Constructive interference:} \\
+ \text{path difference} = n\lambda
+ \end{align*}
-
-
-
-
- \( s = \frac{\lambda D}{d} \)
-
-
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s = \frac{\lambda D}{d}
+
+ Copy LaTeX
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+
+
+
+
+ \begin{align*}
+ \text{Destructive interference:} \\
+ \text{path difference} = (n + \frac{1}{2})\lambda
+ \end{align*}
-
-
- C.3 Wave Phenomena - Additional High Level Content - LaTeX
-
-
- \( \theta = \frac{\lambda}{b} \)
-
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\theta = \frac{\lambda}{b}
+
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+
+
+
+
+
+ C.3 Wave Phenomena - Additional High Level Content - LaTeX
+
+
+
+
+ \( \theta = \frac{\lambda}{b} \)
-
-
- \( n\lambda = d \sin \theta \)
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n\lambda = d \sin \theta
+
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+
+
+ \( n\lambda = d \sin \theta \)
-
-
-
-
- C.2 Wave Model Equations - Basic
-
-
- n₁/n₂ = sin θ₂/sin θ₁ = v₂/v₁
-
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Snell's Law
+
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+
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+
+
+ C.3 Wave Phenomena Equations - Basic
+
+
+
+
n₁/n₂ = sin θ₂/sin θ₁ = v₂/v₁
+
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+
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-
-
-
- Constructive interference:
- path difference = nλ
-
-
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Constructive Interference
-
-
-
-
-
- Destructive interference:
- path difference = (n + ½)λ
-
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Destructive Interference
-
-
-
-
-
- s = λD/d
-
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Single Slit Diffraction
+
+
+
s = λD/d
+
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+
+
+
+
Constructive interference: path difference = nλ
+
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+
+
+
+
Destructive interference: path difference = (n + ½)λ
+
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-
-
- C.3 Wave Phenomena - Additional High Level Content - Basic
-
-
- θ = λ/b
+
+
+
+
+ C.3 Wave Phenomena - Additional High Level Content - Basic
+