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2026-08-20 14:32:36: SHM

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johnruina
2026-08-20 14:32:38 -04:00
parent 4494f376a6
commit 5410f12973
15 changed files with 595 additions and 71 deletions
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- [ ] ⏫ 📅 2026-09-01🛫 2026-08-15 FINISH STUDYING AP BIOLOGY ATLEAST
- [ ] 🔽 FINISH DOING SOMETHING WITH THE ESP 32
- [ ] 🔼 GRAB THAT 3D PRINTER
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[[chemistry of life]]
[[Chemistry of Life]]
6 main elements in biology, chnops
**C**arbon
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[[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
biology/Chemistry of Life/chemistry of life.md
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[[biology]]
chemistry and life somewhat go hand in hand
biology/Chemistry of Life/structure of water and hydrogen bonding.md
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[[chemistry of life]]
[[Chemistry of Life]]
# SUMMARY
## Key Takeaways
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[[Oscillations]]
It's when a restoring force is proportional to the displacement from equilibrium.
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* 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.
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[[Oscillations]]
In an ideal SHM, total mechanical energy stays constant. Kinetic energy peaks at equilibrium, potential peaks at turning points.
# Summary
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* Spring-object system: $E_{total}=\frac{1}{2}kA^2$
* Real systems lose energy to friction and such, lowering oscillation over time.
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[[Oscillations]]
# Summary
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* $T=1/f$
* Mass spring oscillator has period $T=2\pi\sqrt{m/k}$
* Small angle pendulum has period $T=2\pi\sqrt{l/g}$
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[[physics]]
physics/Oscillations/Representing and Analyzing SHM.md
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[[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.
physics/Torque and Rotational Dynamics/Newton's Second Law in Rotational Form.md
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[[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.
physics/Torque and Rotational Dynamics/Rotational Equilibrium and Newton's First Law in Rotational Form.md
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[[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.
physics/Torque and Rotational Dynamics/Rotational Inertia.md
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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)