From 5410f129733d4affbc1e7c2a69d2f0c384ad0083 Mon Sep 17 00:00:00 2001 From: johnruina Date: Thu, 20 Aug 2026 14:32:38 -0400 Subject: [PATCH] 2026-08-20 14:32:36: SHM --- .obsidian/graph.json | 2 +- .obsidian/workspace.json | 593 ++++++++++++++++-- Tasks.md | 3 +- biology/Chemistry of Life/Elements of Life.md | 2 +- biology/Chemistry of Life/Macromolecules.md | 2 +- .../Chemistry of Life/chemistry of life.md | 1 - ...structure of water and hydrogen bonding.md | 2 +- .../Defining Simple Harmonic Motion (SHM).md | 11 + .../Energy of Simple Harmonic Oscillators.md | 10 + .../Frequency and Period of SHM.md | 10 + physics/Oscillations/Oscillations.md | 1 + .../Representing and Analyzing SHM.md | 10 + .../Newton's Second Law in Rotational Form.md | 7 + ...d Newton's First Law in Rotational Form.md | 6 + .../Rotational Inertia.md | 6 + 15 files changed, 595 insertions(+), 71 deletions(-) create mode 100644 physics/Oscillations/Defining Simple Harmonic Motion (SHM).md create mode 100644 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a/biology/Chemistry of Life/Elements of Life.md +++ b/biology/Chemistry of Life/Elements of Life.md @@ -1,4 +1,4 @@ -[[chemistry of life]] +[[Chemistry of Life]] 6 main elements in biology, chnops **C**arbon diff --git a/biology/Chemistry of Life/Macromolecules.md b/biology/Chemistry of Life/Macromolecules.md index 46df57a..77c9d9e 100644 --- a/biology/Chemistry of Life/Macromolecules.md +++ b/biology/Chemistry of Life/Macromolecules.md @@ -1,4 +1,4 @@ -[[biology]] +[[Chemistry of Life]] macromolecules are essentially very large molecules macromolecules consist of smaller subunits, called monomers, when you have a bunch of monomers together it's called a polymer diff --git a/biology/Chemistry of Life/chemistry of life.md b/biology/Chemistry of Life/chemistry of life.md index aed3275..f97ad66 100644 --- a/biology/Chemistry of Life/chemistry of life.md +++ b/biology/Chemistry of Life/chemistry of life.md @@ -1,2 +1 @@ [[biology]] -chemistry and life somewhat go hand in hand \ No newline at end of file diff --git a/biology/Chemistry of Life/structure of water and hydrogen bonding.md b/biology/Chemistry of Life/structure of water and hydrogen bonding.md index 2d9f8bc..96643f6 100644 --- a/biology/Chemistry of Life/structure of water and hydrogen bonding.md +++ b/biology/Chemistry of Life/structure of water and hydrogen bonding.md @@ -1,4 +1,4 @@ -[[chemistry of life]] +[[Chemistry of Life]] # SUMMARY ## Key Takeaways diff --git a/physics/Oscillations/Defining Simple Harmonic Motion (SHM).md b/physics/Oscillations/Defining Simple Harmonic Motion (SHM).md new file mode 100644 index 0000000..9f8e9fe --- /dev/null +++ b/physics/Oscillations/Defining Simple Harmonic Motion (SHM).md @@ -0,0 +1,11 @@ +[[Oscillations]] +It's when a restoring force is proportional to the displacement from equilibrium. + +# Summary +* $F_x=-k\Delta x$ +* Acceleration always points opposite to displacement. +* Equilibrium is where net force is zero. +* Maximum displacement is amplitude. +* Velocity is maximum at equilibrium. +* Pendulum acts as SHM at low angles because restoring force is proportional to angle. + diff --git a/physics/Oscillations/Energy of Simple Harmonic Oscillators.md b/physics/Oscillations/Energy of Simple Harmonic Oscillators.md new file mode 100644 index 0000000..7db7e39 --- /dev/null +++ b/physics/Oscillations/Energy of Simple Harmonic Oscillators.md @@ -0,0 +1,10 @@ +[[Oscillations]] +In an ideal SHM, total mechanical energy stays constant. Kinetic energy peaks at equilibrium, potential peaks at turning points. + +# Summary +* Total mechanical energy in an SHM = $E_{total}=U+K$ +* Spring-object system: $E_{total}=\frac{1}{2}kA^2$ +* Real systems lose energy to friction and such, lowering oscillation over time. + + + diff --git a/physics/Oscillations/Frequency and Period of SHM.md b/physics/Oscillations/Frequency and Period of SHM.md new file mode 100644 index 0000000..c34b133 --- /dev/null +++ b/physics/Oscillations/Frequency and Period of SHM.md @@ -0,0 +1,10 @@ +[[Oscillations]] + + +# Summary +* Period is how long it takes in seconds, frequency is how many times in a second. +* $T=1/f$ +* Mass spring oscillator has period $T=2\pi\sqrt{m/k}$ +* Small angle pendulum has period $T=2\pi\sqrt{l/g}$ +* Pendulum formula only works on small angles (~15$\degree$), larger angles increase period. + diff --git a/physics/Oscillations/Oscillations.md b/physics/Oscillations/Oscillations.md new file mode 100644 index 0000000..5547faf --- /dev/null +++ b/physics/Oscillations/Oscillations.md @@ -0,0 +1 @@ +[[physics]] \ No newline at end of file diff --git a/physics/Oscillations/Representing and Analyzing SHM.md b/physics/Oscillations/Representing and Analyzing SHM.md new file mode 100644 index 0000000..ba1cafd --- /dev/null +++ b/physics/Oscillations/Representing and Analyzing SHM.md @@ -0,0 +1,10 @@ +[[Oscillations]] +# Summary +* $x=A\cos(2\pi ft)$ for when object starts at max displacement (cos(0) = 1) +* $x=A\sin(2\pi ft)$ for when object starts at equilibrium (sin(0) = 0) +* Velocity is largest at equilibrium, acceleration is largest at turning points. +* Amplitude does not affect period. +* Velocity time graphs are shifted by a quarter period from displacement. +* Acceleration time graphs are shifted by half a period. +* Reading zeros and extrema tells position, direction of motion, and whether the object is speeding up or slowing down. + diff --git a/physics/Torque and Rotational Dynamics/Newton's Second Law in Rotational Form.md b/physics/Torque and Rotational Dynamics/Newton's Second Law in Rotational Form.md new file mode 100644 index 0000000..285c98f --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Newton's Second Law in Rotational Form.md @@ -0,0 +1,7 @@ +[[Torque and Rotational Dynamics]] + +# Summary +* Core equation: $a_{sys}=\frac{\tau_{net}}{I_{sys}}$ +* Derived from F=ma +* Angular acceleration is inversely proportional to rotational inertia. +* Angular acceleration is directly proportional to torque. \ No newline at end of file diff --git a/physics/Torque and Rotational Dynamics/Rotational Equilibrium and Newton's First Law in Rotational Form.md b/physics/Torque and Rotational Dynamics/Rotational Equilibrium and Newton's First Law in Rotational Form.md new file mode 100644 index 0000000..94198bd --- /dev/null +++ b/physics/Torque and Rotational Dynamics/Rotational Equilibrium and Newton's First Law in Rotational Form.md @@ -0,0 +1,6 @@ +[[Torque and Rotational Dynamics]] +# Summary +* Rotational equilibrium is keeping angular velocity constant because net torque is zero. +* Rotational equilibrium and translational equilibrium aren't related. +* Use force and FBDs to find all torques. + diff --git a/physics/Torque and Rotational Dynamics/Rotational Inertia.md b/physics/Torque and Rotational Dynamics/Rotational Inertia.md index e195dd7..59aee58 100644 --- a/physics/Torque and Rotational Dynamics/Rotational Inertia.md +++ b/physics/Torque and Rotational Dynamics/Rotational Inertia.md @@ -7,3 +7,9 @@ r is radial distance Several discrete objects: $$I_{tot}=\Sigma I_i=\Sigma m_i r^2$$ +# Parallel Axis Theorem +$$I'=I_{cm}+Md^2$$ +- $I$' is rotational inertia about the parallel axis (kg⋅m²) +- $I_{cm}$ is rotational inertia about the center-of-mass axis (kg⋅m²) +- $M$ is the total mass of the system (kg) +- $d$ is the perpendicular distance between the two parallel axes (m) \ No newline at end of file