A version of this post is also available as a YouTube video here.

In this post I want to look at the physics of a playground swing, and how we can pump it to get higher. There are actually two different methods of pumping a swing: a seated method and a standing method. In my post and video I focus on the seated method.

I used a model from Hirata et al (2023) in which the human body is approximated by three segments, and the chain of the swing is assumed to remain straight. I took the Euler-Lagrange equation from the paper, with minor fixes¹, and ran it forward in time using a Runge-Kutta method. My source code is available here and includes the parameters I used.

A version of this post is also available as a YouTube video here.

Recently, while working on my upcoming post about the physics of playground swings, I was analyzing the mechanics of a double pendulum system similar to the following:

The motion of the lower limb can be thought of as a superposition of two rotational motions, ω₀ around one axis and ω₁ around another axis. It got me thinking about how to write down the kinetic energy of such a superposition.

In part 1 and part 2, we introduced the reverse sprinkler problem and tried to gain some theoretical insight. In this final part, we will simulate five different sprinkler designs and interpret the torque results.

In part 1, we introduced the reverse sprinkler problem and attacked the most ideal case, ignoring factors such as pipe diameter. Now we will perform a more general analysis.

A short version of this post series is also available as a YouTube video here.

The reverse sprinkler is a physics problem that has long been a source of confusion and debate. It is sometimes known as the Feynman sprinkler problem after Richard Feynman who popularized it. Briefly: consider the type of garden sprinkler that rotates as water is ejected from it. Now submerse the sprinkler in a tank and reverse the fluid flow such that water is sucked in instead of ejected. Does the sprinkler rotate, and if so, in which direction?

A short version of this post is also available as a YouTube video here.

Is it possible to build a wind-powered vehicle that can continuously travel faster than the wind, in the same direction as the wind?

Like the airplane-on-treadmill problem and the Feynman sprinkler problem, this question has spawned endless Internet arguments. In 2010, Rick Cavallaro and team demonstrated a vehicle called Blackbird that officially reached a speed of 2.7 times the wind speed. But this just spawned more arguments. Indeed the design, in which the wheels are geared to a propeller, has all of the hallmarks of a perpetual motion machine, so it is understandable that some are skeptical. Here I want to present a thought experiment that might help to clarify some of the physics by reference to something more familiar: an airplane.

Electromagnetic radiation is something that has often eluded my intuition. Electrical engineering depends on numerous abstractions: current flowing in wires like a fluid, capacitance/inductance in lieu of near field interactions, antenna theory to model far field interactions, etc. These abstractions are essential to make electromagnetic theory tractable for everyday use. But they also obscure the underlying physics and can result in incorrect conclusions when reality crosses the boundaries of the abstractions.

Looking at electromagnetic radiation from first principles provides, I think, some interesting insights. In this blog post I show how the phenomenon of radiation can be derived from little more than basic special relativity (which itself follows from only a small number of postulates about the universe). This is not new but I think many readers may not be aware of it.

You may have heard of the incident where a helium leak suddenly disabled many iPhones at a medical facility. The root cause — tiny MEMS oscillators being susceptible to helium leaking into their hermetically-sealed casings — is interesting but not especially surprising. Helium is the second lightest element in the periodic table; helium atoms are tiny and have a knack for diffusing through all sorts of barriers.

What is very interesting, though, is that the helium exposure causes the frequency of the oscillator to go up rather than down (at least initially before more serious failures occur). In an experiment performed in a YouTube video from Applied Science, the frequency increases from 32768.24 Hz to 32768.70 Hz (14 parts per million) before device failure. In a research paper, which exposes a (different) MEMS oscillator to helium at high pressure over 50 hours, the frequency increases from 30418 Hz to 30501 Hz which is over 2700 ppm!

If the oscillators weren’t hermetically sealed, then the frequency increase would be understandable — helium is lighter than air, and we all know what happens when we breathe in helium. But normally the oscillators are under near-vacuum conditions. Intuitively one would expect the addition of helium atoms to slow down the oscillation, either via gas damping or mass increase. Neither the YouTube video nor the mentioned research paper explain why the frequency increases.

For a long time I thought of the H field as being generated by free currents only. The problem with this view is that it leads us to make erroneous assumptions. We know from the definition of H that:

The magnetization M is 0 outside of a material. So if we assume that H is due to free currents only, one would conclude that the magnetic field/flux B outside a material is also a function of free currents only – e.g. the external magnetic field of a solenoid would be independent of the material the core is made of. However, as seen in my previous post, this is not true. Also, one might conclude that permanent magnets have no external magnetic field, which is clearly not true either…!