5 More Physics Equations Everyone Should Know

https://fed.brid.gy/r/https://www.wired.com/story/5-more-physics-equations-everyone-should-know/

Demonstrating Problem Solving - Gravitational Potential Energy

https://media.cooleysekula.net/w/wDeC2X6zGqCirY48EU4wSu

A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).

Background:
The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.

In more detail:
A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).

#Pendulum #Cycloid #Period #Frequency #SHM #TimePeriod #CycloidalPendulum #Lagrange #Cusp #Energy #KineticEnergy #PotentialEnergy #Lagrangian #Length #Math #Maths #Physics #Mechanics #ClassicalMechanics #Amplitude #CircularFrequency #Motion #Vibration #HarmonicMotion #Parameter #ParemeterizedEquation #GoverningEquations #Equation #Equations #DifferentialEquations #Calculus

💥 https://thekidshouldseethis.com/post/popsicle-stick-cobra-weave-chain-reaction-video-compilation

From the American Journal of #Physics: "When weaving the chain, one realizes that a large #potentialenergy is stored in the sticks, and the ends of the chain must be held still by using a weight or one’s hand… When one end of the chain is released, the so-called ‘#stickbomb’ detonates—the potential energy is released as the sticks pop up and a traveling #wave is formed…”

#video #chainreaction #domino #popsiclesticks #science #activities #play #hevesh5 #compilation

Capitalists: The Potential Energy of Human Productivity

The Austrian theory of capital is the best one you can find if you really want to grasp how the economy actually works—beyond sterile mathematics and static timeless analysis.

https://indianlibertyreport.com/capitalists-the-potential-energy-of-human-productivity/

#capitalism #potentialenergy #ProductionTheory