# Teaching Resources

Physics teaching resources

## Tensegrity Explained

There is a new internet trend called “tensegrity” – an amalgamation of the words tension and integrity. It is basically a trend of videos showing how objects appear to float above a structure while experiencing tensions that appear to pull parts of the floating object downwards.

In the diagram below, the red vectors show the tensions acting on the “floating” object while the green vector shows the weight of the object.

The main force that makes this possible is the upward tension (shown below) exerted by the string from which the lowest point of the object is suspended. The other tensions are downward and serve to balance the moment created by the weight of the object. The centre of gravity of the “floating” structure lies just in front of the supporting string. The two smaller downward vectors at the back due to the strings balance the moment due to the weight, and give the structure stability sideways.

This is a fun demonstration to teach the principle of moments, and concepts of equilibrium.

The next image labels the forces acting on the upper structure. Notice that the centre of gravity lies somewhere in empty space due to its shape.

These tensegrity structures are very easy to build if you understand the physics behind them. Some tips on building such structures:

1. Make the two strings exerting the downward tensions are easy to adjust by using technic pins to stick them into bricks with holes. You can simply pull to release more string in order to achieve the right balance.
2. The two strings should be sufficiently far apart to prevent the floating structure from tilting too easily to the side.
3. The centre of gravity of the floating structure must be in front of the string exerting the upward tension.
4. The base must be wide enough to provide some stability so that the whole structure does not topple.

Here’s another tensegrity structure that I built: this time, with a Lego construction theme.

Apart from using Lego, I have also 3D-printed a tensegrity structure that only requires rubber bands to hold up. In this case, the centre of gravity of the upper structure is somewhere more central with respect to the base structure. Hence, 3 rubber bands of almost equal tension will be used to provide the balance. The STL file for the 3D model can be downloaded from Thingiverse.com.

The main challenge in assembling a tensegrity structure is the adjustment of the tensions such that the upper structure is balanced. One way to simplify that, for beginners, is to use one that is supported by rubber bands as the rubber bands can adjust their lengths according to the tensions required.

Another tip is to use some blu-tack instead of tying the knots dead such as in the photo below. This is a 3D printed structure, also from Thingiverse.

(This post was first published on 18 April 2020 and is revised on 24 August 2022.)

## A list of Physics websites by Singapore teachers

I had the pleasure of making the acquaintance of a fellow Singaporean physics teacher who has also created his own website to host his teaching and learning resources at ThePhysicsGrove.com. He had managed to complete coverage of the O level Physics syllabus in a series of YouTube videos and I see that he is also creating Google Quizzes, Quizzizz and Kahoots for some topics.

I thought this will be a good opportunity to list down the various websites that I have been following because students will find them useful as well. Among the authors are Evan Toh (whom I met at ICTLT), a talented artist who infused comic drawing in the explanation of physics concepts, and Lawrence Wee, a friend and mentor who got me started on making javascript simulations.

1. XMPhysics (for A-level students) – by Hwa Chong Institution teacher, Chua Kah Hean at https://xmphysics.com
2. Evan’s Space (for O-level students) – by Edgefield Secondary School teacher, Evan Toh at https://evantoh23.wordpress.com/
3. The Physics Grove (for O-level students) – by Hillgrove Secondary School teacher, Jonathan Ho at https://www.thephysicsgrove.com/
4. Open Educational Resources (for all students) – by Senior Specialist, Lawrence Wee at https://iwant2study.org/ospsg/

I feel that it is necessary to maintain this list because a casual search for Physics websites in Google will return the dozens of tuition service providers (some of which are run by my ex-colleagues!) rather than these free-to-use learning resources that have been created. Hopefully with these backlinks, Google’s search algorithm will direct more traffic to such websites in future, although I still don’t think we can compete against the competitive tuition industry in terms of search engine optimisation. At least, one can find them through this page.

If you happen to come across any other similar websites, please leave a comment below or let me know personally if you know me.

## Famous Physicists according to topic

To incorporate elements of the Nature of Science in our teaching, we often talk about some of the scientists who have contributed to the discoveries that led to an understanding of the universe, the circumstances and constraints they face, and their attitudes and values. This is an incomplete list of some of the scientists who have their names prominently featuring either as a unit of measure or in a law of physics, classified by the A-level topics. I am compiling this as a quick reference for lesson planning purposes.

Dynamics

• Sir Isaac Newton (1643-1703 English) – Newton’s laws of motion, Newton’s law of gravitation

Forces

• Archimedes of Syracuse (287-212 BC Greek) – principle of the lever, law of buoyancy
• Robert Hooke (1635-1703 English) – Hooke’s law

Energy, Work and Power

• James Watt (1736-1819 Scottish) – improved efficiency of steam engines
• James Prescott Joule (1818-1889 English) – discovered mechanical equivalent of heat

Thermal Physics

• Anders Celsius (1701-1744 Swedish) – proposed (an inverted form of) the Centigrade temperature scale
• Robert Brown (1773-1858 Scottish) – botanist who observed Brownian motion
• Lord Kelvin (1824-1907 British) – formulated first and second laws of thermodynamics
• Ludwig Eduard Boltzmann (1844-1906 Austrian) – statistical explanation of second law of thermodynamics, defined entropy

Wave Motion and Superposition

• Étienne-Louis Malus (1775-1812 French) – discovered polarization of light by reflection, double refraction of light in crystals
• Wilhelm Conrad Röntgen (1845-1923 German) – discovered X-rays by accident
• Heinrich Hertz (1857-1894 German) – proved the existence of the electromagnetic waves
• Lord Rayleigh (1842-1919 English) – Rayleigh’s criterion for angular resolution

Electric Fields, Current Electricity and DC Circuits

• Charles-Augustin de Coulomb (1736-1806 French) – discovered Coulomb’s law
• Count Alessandro Volta (1745-1827 Italian) – invented first electric battery
• Andre Marie Ampere (1775-1836 French) – electrodynamics
• Georg Ohm (1789-1854 German) – discovered that current flow is proportional to p.d. and inversely proportional to resistance
• Benjamin Franklin (1785-1788 American) – discovered principle of conservation of charge, kite experiment

Electromagnetism

• Hans Christien Oersted (1777-1851 Danish) – discovered that electric currents create magnetic fields
• Sir John Ambrose Fleming (1849-1945 English) – professor of electrical engineering, establised right-hand rule

Electromagnetic Induction

• Michael Faraday (1791-1867 English) – discovered principle of electromagnetic induction
• Heinrich Friedrich Emil Lenz (1804-1865 German) – formulated Lenz’s law

Alternating Current

• Nikola Tesla (1856-1943, Austrian/American) – designed modern AC supply system

Modern Physics

• Max Karl Planck (1858-1947 German) – quantum theory
• Albert Einstein (1879-1955 German/Swiss/American) – mass-energy equivalence, photoelectric effect, etc.
• Louis de Broglie (1892-1987 French) – wave nature of electrons
• Werner Karl Heisenberg (1901-1976 German) – pioneer in quantum mechanics, uncertainty principle

Nuclear Physics

• Henri Becquerel (1852-1908 French) – discovered evidence of radioactivity
• Pierre Curie (1859-1096 French) – pioneer in radioactivity
• Marie Curie (1867-1934 Polish/French) – pioneer in radioactivity, only woman to win Nobel Prize twice

## Bouncing Ball Animation using Python

For a fullscreen view, visit https://www.glowscript.org/#/user/wboson2007/folder/MyPrograms/program/Bouncing

Modified this python simulation from Dr Darren Tan’s work at https://sciencesamurai.trinket.io/a-level-physics-programming#/collisions/bouncing-ball

Wanted to try out a different way of creating simulations. Added the acceleration-time graph in place of his energy-time graph, in preparation for the teaching of kinematics. Also assuming no energy loss during collisions for simplicity.

For Singapore teachers, I have submitted a request to SLS for this URL to be whitelisted for embedding. Once approved, glowscript simulations can be embedded as part of the lesson. For the time being, a URL link out to the simulation will have to do.

## 3D Virtual Experiment – Simple Pendulum

This is a simple virtual experiment with a 3D view, allow teachers to explain the simple concepts of an oscillation experiment, such as which view is best to measure timing of the oscillation from.

To access this simulation directly via GeoGebra, go to : https://www.geogebra.org/m/d3yxgjfp

To embed it in SLS or other platforms, use the following code:

<iframe scrolling="no" title="Pendulum" src="https://www.geogebra.org/material/iframe/id/d3yxgjfp/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/true/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

## 3D Virtual Experiment on Torsional Pendulum

In preparation for HBL in 2022, I designed a simple virtual experiment that will allow for students to collect data on oscillations using their own stopwatches and investigate the relationship between the period of oscillation and two separate variables. To access the simulation on GeoGebra, visit https://www.geogebra.org/m/jhc4xvpe.

Based on the given relationship $$T = cm^aL^b$$ where a, b and c are constants, students will be tasked to find the constants a, b and c. Students will then attempt to “linearise” the equation such that the independent variables m and L can be tested one by one.

Examples of data collected can be plotted using Excel to give the following graphs from which the gradients and vertical intercepts can be obtained instantly.