https://gdpark.blog/categories/physics/Recent content in Physics on gdpark.blogHugoenMon, 06 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-01-vectors-and-polar-coordinates/Thu, 18 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-01-vectors-and-polar-coordinates/A breezy walkthrough of cross products, the BAC-CAB rule, coordinate transformation matrices, and polar coords — all the vector stuff that actually felt new in university physics.https://gdpark.blog/posts/classical-mechanics-02-work-energy-theorem-and-conservative-forces/Thu, 18 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-02-work-energy-theorem-and-conservative-forces/Sneakily deriving the Work-Energy Theorem from Newton’s second law via the chain rule, then defining potential energy and unpacking what conservative forces actually are!https://gdpark.blog/posts/classical-mechanics-03-oscillations-and-damped-harmonic-motion/Fri, 19 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-03-oscillations-and-damped-harmonic-motion/Zoom in on literally any potential with a Taylor expansion and BAM — it’s a spring, which is why oscillations pop up absolutely everywhere in physics.https://gdpark.blog/posts/classical-mechanics-04-forced-harmonic-oscillation-and-resonance/Sat, 20 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-04-forced-harmonic-oscillation-and-resonance/What happens when the driving frequency hits just right? We work through forced harmonic oscillation — no damping first, then with resistance — to see why resonance is so wild.https://gdpark.blog/posts/classical-mechanics-05-2d-and-3d-isotropic-harmonic-oscillators-and-lissajous-figur/Mon, 22 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-05-2d-and-3d-isotropic-harmonic-oscillators-and-lissajous-figur/Jumping into the 2D/3D isotropic harmonic oscillator, separating equations of motion and eliminating t to uncover the elliptical paths and Lissajous figures hiding inside!https://gdpark.blog/posts/classical-mechanics-06-inertial-and-non-inertial-frames-and-the-galilean-transforma/Tue, 23 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-06-inertial-and-non-inertial-frames-and-the-galilean-transforma/Turns out Newton’s first law isn’t obvious at all — it’s secretly guaranteeing that inertial frames exist, and that’s the whole setup for the Galilean transformation.https://gdpark.blog/posts/classical-mechanics-07-rotating-reference-frames-coriolis-transverse-and-centrifuga/Wed, 24 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-07-rotating-reference-frames-coriolis-transverse-and-centrifuga/We figure out the discrepancy between a stationary frame and a purely-rotating one — and that’s exactly where Coriolis, centrifugal, and transverse forces come from!https://gdpark.blog/posts/classical-mechanics-08-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-08-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/A breezy Newton sidebar on universal gravitation sets the stage for Kepler’s laws — including a quick sanity check on whether treating planets as point masses is actually legit, heh.https://gdpark.blog/posts/classical-mechanics-09-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-09-kepler-s-laws-ellipse-law-equal-area-law-and-harmonic-law-pa/We derive the polar equation of an ellipse straight from its definition, then match it to the orbital equation — and yeah, gravity really does give you ellipses!!!https://gdpark.blog/posts/classical-mechanics-10-the-orbit-equation-via-energy-methods/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-10-the-orbit-equation-via-energy-methods/We re-derive the orbital equation using energy conservation instead of angular momentum — plus a quick vibe check on why gravitational potential energy is negative.https://gdpark.blog/posts/classical-mechanics-11-orbital-stability/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-11-orbital-stability/Why does Earth just keep cruising in its orbit without getting knocked off track? Turns out there’s a sneaky spring constant hiding in the radial equation of motion!https://gdpark.blog/posts/classical-mechanics-12-series-quick-reference-overview/Thu, 25 Jun 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-12-series-quick-reference-overview/A handy visual quick-reference overview for the series, packed with everything you need at a glance.https://gdpark.blog/posts/classical-mechanics-13-center-of-mass-cm/Fri, 07 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-13-center-of-mass-cm/Breaking down the center of mass — turns out it’s just a mass-weighted average of particle positions, and yeah, once you see it that way it actually makes sense.https://gdpark.blog/posts/classical-mechanics-14-momentum-of-a-system-of-particles/Fri, 07 Nov 2014 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-14-momentum-of-a-system-of-particles/We sum momenta across a whole system of particles, watch internal forces cancel out via Newton’s third law, and land smack on conservation of linear momentum.https://gdpark.blog/posts/classical-mechanics-15-angular-momentum-of-a-system-of-particles/Sat, 17 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-15-angular-momentum-of-a-system-of-particles/We decompose total angular momentum into an orbital piece (system as one lump at the CM) and a spin piece (particles wiggling around it) — and show why those cross terms vanish.https://gdpark.blog/posts/classical-mechanics-16-rigid-body-dynamics-and-the-center-of-mass-of-a-rigid-body/Sat, 17 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-16-rigid-body-dynamics-and-the-center-of-mass-of-a-rigid-body/We swap the sigma for an integral and hunt down the center of mass of a rigid body — basically a particle system with locked spacing — then crunch through a solid hemisphere and a shell.https://gdpark.blog/posts/classical-mechanics-17-moment-of-inertia-perpendicular-axis-theorem-and-parallel-ax/Sun, 18 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-17-moment-of-inertia-perpendicular-axis-theorem-and-parallel-ax/A casual, build-it-up walkthrough of moment of inertia for flat rigid bodies, covering why it acts like rotational mass and how the perpendicular and parallel axis theorems let you shift between axes.https://gdpark.blog/posts/classical-mechanics-18-radius-of-gyration/Sun, 18 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-18-radius-of-gyration/Breaking down what the radius of gyration k actually is — why we square distances, what dividing by mass really does, and how k is just the mean of squared distances laid bare.https://gdpark.blog/posts/classical-mechanics-19-physical-pendulum-and-center-of-oscillation/Sun, 18 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-19-physical-pendulum-and-center-of-oscillation/A casual walkthrough of how a rigid body swings as a physical pendulum, and why its period maps neatly onto the classic simple pendulum formula via the radius of gyration.https://gdpark.blog/posts/classical-mechanics-20-rigid-body-in-planar-motion/Mon, 19 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-20-rigid-body-in-planar-motion/Fixed-axis rotation is so last chapter — now the axis itself moves, and we figure out exactly when that messy extra torque term thankfully drops to zero.https://gdpark.blog/posts/classical-mechanics-21-three-dimensional-motion-of-a-rigid-body/Mon, 19 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-21-three-dimensional-motion-of-a-rigid-body/We level up from flat pancakes to sweet potatoes — spinning a 3D rigid body on an arbitrary axis and cooking up the full inertia tensor from direction cosines.https://gdpark.blog/posts/classical-mechanics-22-the-inertia-tensor/Tue, 20 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-22-the-inertia-tensor/A casual, honest walkthrough of finally grokking the moment of inertia tensor — what tensors actually are, why they’re ‘absolute’, and how the matrix form works.https://gdpark.blog/posts/classical-mechanics-23-principal-axes-of-a-rigid-body/Wed, 21 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-23-principal-axes-of-a-rigid-body/A fun intro to principal axes of a rigid body — why they matter, how products of inertia vanish, and all the notation conventions that come with them.https://gdpark.blog/posts/classical-mechanics-24-euler-s-equations-of-motion-for-a-rigid-body/Thu, 22 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-24-euler-s-equations-of-motion-for-a-rigid-body/We finally dig into full-on 3D rigid body rotation — inertial frames, rotating frames, and how Euler’s equations of motion fall out of it all. lol.https://gdpark.blog/posts/classical-mechanics-25-euler-angles/Fri, 23 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-25-euler-angles/Breaking down Euler angles — theta, phi, and psi — and how three coordinate systems team up to fully describe a spinning top’s orientation in space.https://gdpark.blog/posts/classical-mechanics-26-euler-angles-part-2/Sat, 24 Jan 2015 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-26-euler-angles-part-2/Breaking down the angular velocity vector into spin, nutation, and precession — yes, I hate just swallowing equations, but here we go anyway.https://gdpark.blog/posts/classical-mechanics-27-angle-between-the-ellipse-axis-and-the-x-axis/Mon, 06 Nov 2017 00:00:00 +0000https://gdpark.blog/posts/classical-mechanics-27-angle-between-the-ellipse-axis-and-the-x-axis/Finally worked out the actual derivation for the angle ψ the ellipse’s major axis makes with the x-axis — something my textbook just handed me without proof and I never questioned until now.