GeoGebra Posts

While I have shared a simulation of a bouncing ball made using Glowscript before, I felt that one made using GeoGebra is necessary for a more comprehensive library. It took a while due to the need to adjust the equations used based on the position of the graphs, but here it is: https://www.geogebra.org/m/dfb53dps The kinematics of ...

Direct link: https://www.geogebra.org/m/u2m3gnzj The above is a GeoGebra applet that can be customised for any energy problem. Simply make a copy of it and change the values or labels as needed. This can be integrated into either GeoGebra Classroom or Google Classroom (as a GeoGebra assignment) and the teacher can then monitor every student’s attempt ...

My third applet today is a self-assessment tool for students to practise calculations with Snell’s Law, i.e. $n_1 \sin{\theta_1} = n_2 \sin{\theta_2}$. The direct link to the applet is https://www.geogebra.org/m/fhmmuhbg Snell’s law, also known as the law of refraction, describes how light waves change direction as they pass from one medium to another with different refractive indices. ...

I have seen a few simulations for apparent depth but was not satisfied with them. So I created this from scratch for use in tomorrow’s lesson. The positions of the eye and image of the fish are adjustable. It is more challenging to design for the actual fish to be draggable, so I only could ...

This applet allows for students to visualise the conditions under which a reflection can be seen in a mirror. When the mirror is too short, for instance, the point of reflection does not lie on the mirror so light cannot be reflected. Link here: https://www.geogebra.org/m/rjpb2dv7

Direct link to GeoGebra: https://www.geogebra.org/m/e87sbuy8 I translate the wonderful applet done by Gilles Claudel at https://www.geogebra.org/m/AXY9QRs5 from French into English and customised it for the Singapore curriculum.

This is a common example used in the JC1 topics of Oscillations, where if one were to look at an object moving in circles from the side view, it will appear to move in simple harmonic motion. This simple 3D animation allows users to rotate the view to see exactly that. Right click and drag ...

This displacement-time graph is used in conjunction with an SLS package to help students learn how to describe motion of an object and to use gradient of a tangent to calculate the magnitude of velocity. For a direct link to the app, go to https://www.geogebra.org/m/k3ja7bnm I added a little spider to help students visualise the movement ...

I made some refinement to an applet created last year to demonstrate how vector addition can be done either using vector triangle or parallelogram methods. To access directly in Geogebra, the link is https://www.geogebra.org/m/p2yvdsvs

This new applet is designed for students to practise conversion of common units used in physics on their own. There is a checking algorithm within, which might need some fine-tuning. For full screen view, click here. The worked solutions given will demonstrate the breakdown of steps that could help students learn the procedure to convert ...

This little applet is designed to allow students to change the order of magnitude and to use any common prefix to observe how the physical quantities are being written. To view this applet in a new tab, click here. Standard form (also known as scientific notation) is a way of writing very large or very ...

This interactive is designed to help students understand the statistical approach underpinning the drawing of a best-fit line for practical work. For context, our national exams have a practical component where students will need to plot their data, often following a linear trend, on graph paper and to draw a best-fit line to determine ...

Did this simple interactive upon request by a colleague who is teaching the JC1 topic of Oscillations. Based on the following question, this is used as a quick visual to demonstrate why there must be a minimum depth before the boat approaches harbour. The rise and fall of water in a harbour is simple harmonic. The ...

https://www.geogebra.org/m/pmatpapk This applet highlights the parts of a circuit that becomes live depending on the state of a switch and the type of electrical fault in a device. It also demonstrates the roles of the fuse and earth wire in preventing accidents.

https://www.geogebra.org/m/puvfjxk5 This applet demonstrates how terminal potential difference (as measured by the voltmeter across the terminals of the battery) changes depending on : internal resistance r external resistance R emf E when a switch is turned on and off <iframe scrolling="no" title="Internal Resistance and Terminal Potential Difference" src="https://www.geogebra.org/material/iframe/id/puvfjxk5/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/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

https://www.geogebra.org/m/wavar9bx This is a wonderful applet created by Abdul Latiff, another Physics teacher from Singapore, on how air resistance varies during a sky-dive with a parachute. It clearly demonstrates how two different values of terminal velocity can be achieved during the dive. Incidentally, there is a video on Youtube that complements the applet very well. I ...

The wonderful thing about GeoGebra is that you can whip up an applet from scratch within an hour just before your lesson and use it immediately to demonstrate a concept involving interdependent variables. I was motivated to do this after trying to explain a question to my IP4 students. The RGB colours of the thermistor reflects ...

For a full-screen view, click here. <iframe scrolling="no" title="Dynamics Problem" src="https://www.geogebra.org/material/iframe/id/uthszwjq/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> This applet was designed with simple interactive features to adjust two opposing forces along the horizontal direction in order to demonstrate the effect on acceleration and velocity.

Access the app in full screen here: https://www.geogebra.org/m/mfvvhjrj This app is designed to give students practice in interpreting velocity-time graphs with various scenarios, such as more complex examples involving negative velocity and acceleration. Answers will be given if student is wrong. Use this to embed into SLS or another LMS. <iframe scrolling="no" title="Equations of Motion" src="https://www.geogebra.org/material/iframe/id/mfvvhjrj/width/700/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/false/rc/false/ld/false/sdz/false/ctl/false" width="700px" ...

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 ...

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 $$T = cm^aL^b$$ ...

One common misconception among new learners of kinematics is that acceleration of an object being thrown upward is zero at the top of the path when it is momentarily at rest. I created this interactive, along with the 3 graphs in order to help students relate the vectors to the graphical representation of motion. It ...

Access via https://www.geogebra.org/m/erehat7n for a full-screen view.

After completing the vernier calipers applet, I simply had to do a similar one for the micrometer. However, this was a lot more complex as the thimble’s numbers are supposed to be “rotating” rather than moving linearly. A lateral movement of the thimble had to be coupled with a vertical movement of the rotating ...

The aim of this applet is to help students who just learnt about zero errors in vernier calipers to get some practice of their own. Students just have to key in their answer into the textbox and they will know if they got it correct. To modify later: an option to give the correct ...

Having started with making interactive simulations or visualisation apps with Easy JavaScript Simulations (EJsS) under the guidance of Senior Specialist Lawrence Wee from ETD in Nov 2016, I next learnt about GeoGebra in 2017 from my ETD colleagues who taught Math (shoutout to Loh Yan Xiang and Toh Wee Teck). I would like to share ...

The following GeoGebra interactives demonstrate the first few harmonics of an open pipe and a closed pipe given a fixed velocity of sound (340m/s). The frequencies and wavelengths are auto-calculated. Length of the pipe can be varied. Feel free to use, copy or edit them. Open Pipe Source: https://www.geogebra.org/m/tsufws72 For embedding into SLS or other websites: <iframe scrolling="no" ...

This GeoGebra interactive allows students to vary the position of the centre of gravity of a shelf in order to observe the changes of the other two force vectors. The position of the supporting cable can be adjusted too. The ability to resolve vectors allows students to apply principle of moments to understand how the ...

Access in full screen here: https://www.geogebra.org/m/xbknrstt I modified the progressive sound wave interactive into a stationary wave version. This allows students to visualise the movement of particles about a displacement node to understand why pressure antinodes are found there. Usually I will pose this question to students: where would a microphone pick up the loudest sound ...

As a means of visualising what happens to the potential difference, current and power dissipated in an alternating current circuit with half-wave rectification, I have created the interactive applet with all 3 graphs next to each other. It should be easy for students to see that with half-wave rectification, the power dissipated is half that ...

The concept of root-mean-square values for Alternating Currents is challenging if students are to relate the I-t graph with the Irms value directly. They have to be brought through the 3 steps before arriving at the Irms value. This interactive applet allows them to go through step by step and compare several graphs at one time ...

This GeoGebra applet was modified from an existing applet to show the relationship between the pressure-distance and displacement-distance graph of a progressive longitudinal wave.

I have added two more graphs into the interactive animation. However, the app has become a bit sluggish when changing the period or amplitude. It still works smoothly when viewing the animation. Students ought to find it useful to look at all the graphs together instead of in silo. This way, they can better understand ...

Here’s my attempt at animating 5 graphs for simple harmonic motion together in one page. From left column: $$v = \pm\omega\sqrt{x_o^2-x^2}$$ $$a = -\omega^2x$$ From right column: $$s = x_o\sin(\omega t)$$ $$v = x_o\omega \cos(\omega t)$$ $$a = -x_o\omega^2 \sin(\omega t)$$ And here is the animated gif file for powerpoint users:

The first of two apps on Phase Difference allows for interaction to demonstrate the oscillation of two different particles along the same wave with a variable phase difference. The second shows two waves also with a phase difference. In both cases, the phase difference $\Delta\phi$ can be calculated with $$\Delta\phi = \dfrac{\Delta x}{\lambda} \times 2\pi$$ where ...

I modified Tom Walsh’s original GeoGebra app to add a moveable single oscillating particle for students to observe its movement along a longitudinal wave and a transverse wave. The app can also be used to show how the displacement of a particle in a longitudinal wave can be mapped onto a sinusoidal function, similar to the ...

This GeoGebra app allows students to observe closely the movement of a particle in a progressive wave, with two possible directions of energy propagation. In a typical question, students will be asked to predict the next movement of a particle given that a wave is moving left or right. Usually, students will need to imagine ...

https://www.youtube.com/watch?v=Bi7fvcfTBB0 Using a chain of rubber bands, I swung a ball around in a vertical loop. This demonstration shows how the tension in an elastic band changes according to the position of the ball, by referring to the length of the elastic band. Securing the elastic band to the ball with a shoelace When the ball of mass ...

Using the GeoGebra app above, I intend to demonstrate the relationship between total energy, kinetic energy and gravitational potential energy in a rocket trying to escape a planet’s gravitational field. By changing the total energy of the rocket, you will increase the initial kinetic energy, thus allowing it to fly further from the surface of ...

Here is a template that I might use to generate questions for students’ self-assessment in future. Based on a query that one of the participants in a GeoGebra online tutorial asked about generating random questions for simple multiplication for lower primary students. The online tutorial was conducted by some teachers in the Singapore MOE GeoGebra community ...

This GeoGebra app shows how angular velocity ω is the rate of change of angular displacement (i.e. $\omega=\dfrac{\theta}{t}$) and is dependent on the speed and radius of the object in circular motion (i.e. $v=r\omega$). Students can explore the relationships by doing the following: Keeping r constant and varying ω. Keeping ω constant and varying r. Keeping v constant ...

This GeoGebra app shows the relationship s = rθ. One activity I get students can do is to look at the value of θ when the arc length s is equal to the radius r. This would give the definition of the radian, which is the angle subtended at the centre of a circle by an ...

While preparing to share with some fellow teachers in Singapore about the use of GeoGebra in Physics, I came up with a set of simple instructions to create an interactive, while introducing tools such as sliders, checkboxes (along with boolean values) and input boxes. Download it here. You should be able to follow the instructions in ...

While preparing for a bridging class for those JAE JC1s who did not do pure physics in O-levels, I prepared an app on using a vector triangle to “solve problems for a static point mass under the action of 3 forces for 2-dimensional cases”. For A-level students, they can be encouraged to use either the ...

It’s Day 1 of the full home-based learning month in Singapore! As teachers all over Singapore scramble to understand the use of the myriad EdTech tools, I have finally come to settle on a few: Google Meet to do video conferencing Google Classroom for assignment that requires marking Student Learning Space for students’ self-directed learning, collaborative discussion and ...

Problems involving two bodies moving together usually involve asking for the magnitude of the force between the two. For example: A 1.0 kg and a 2.0 kg box are touching each other. A 12 N horizontal force is applied to the 2.0 kg box in order to accelerate both boxes across the floor. Ignoring friction, determine: (a) ...

In an introductory sharing for the use of GeoGebra to my colleagues, I have prepared a simple template for them to try their hands at animations of points and other elements. You can try the same too. Create a moving point by typing into the Input field (5,5*sin(time)) so that you get a point at ...

Through this GeoGebra app, students can observe how the gradient of the displacement-time graph gives the instantaneous velocity and how the area under the velocity-time graph gives the change in displacement. In the GeoGebra app below, you will see a displacement-time graph on the left and its corresponding velocity-time graph on the right. These graphs will ...

This GeoGebra app allows students to observe the difference between instantaneous and average velocity from a graphical perspective.

This GeoGebra app allows users to change the magnitude and direction of the force acting on an object, as well as the initial velocity. The change in kinetic energy is calculated along with the work done in the direction of the force. This demonstrates a very important concept in Physics known as the Work-Energy Theorem, where the ...

The following GeoGebra app simulates the force vectors on an object in uniform vertical circular motion. A real world example of this would be the forces acting on a cabin in a ferris wheel. <iframe scrolling="no" title="Vertical Uniform Circular Motion " src="https://www.geogebra.org/material/iframe/id/t5jstqsm/width/640/height/480/border/888888/sfsb/true/smb/false/stb/false/stbh/false/ai/false/asb/false/sri/true/rc/false/ld/false/sdz/false/ctl/false" width="640px" height="480px" style="border:0px;"> </iframe>

This is a simulation that shows the vectors of forces acting on an object rolling in a vertical loop, assuming negligible friction. To complete the loop, the initial velocity must be sufficiently high so that contact between the object and the track is maintained. When the contact force between the object and its looping track no ...

This GeoGebra app is a 3-D visualisation tool of the force vectors acting on an aircraft turning with uniform circular motion in a horizontal plane. I prepared this in advance as I will be lecturing on this JC1 topic next year.

This app is used to demonstrate how a spherical object with a finite volume immersed in a fluid experiences an upthrust due to the differences in pressure around it. Given that the centre of mass remains in the same position within the fluid, as the radius increases, the pressure due to the ...

I created a series of GeoGebra apps for the JC topics of Waves and Superposition, mainly on the concept of Phase Difference. The sizes of these GeoGebra apps are optimised for embedding into SLS. When I have time, I will create detailed instructions on how to create such apps. Meanwhile, feel free to use them. ...

Useful Links for Learning about using GeoGebra in SLS. Instructions on how to embed GeoGebra into SLS via iframe (recommended) (Method 1). Instructions on how to upload GeoGebra into SLS as a standalone package (Method 2). GeoGebra apps curated for A-level Physics: https://www.geogebra.org/m/dgedzmz3 GeoGebra apps curated for O-level Physics: https://www.geogebra.org/m/z5nfs8qd Using GeoGebra Group as an LMS. IPSG Poster on “An SLS Learning Experience ...

I created a new GeoGebra app based on an ideal Stirling Cycle (A. Romanelli Alternative thermodynamic cycle for the Stirling machine, American Journal of Physics 85, 926 (2017)) which includes two isothermal and two isochoric processes. The Stirling engine is a very good example to apply the First Law of Thermodynamics to, as the amount of ...

Teachers in Singapore have been provided with the Student Learning Space (SLS) – an online platform meant for students’ self-directed learning using MOE’s curriculum-aligned resources as well as for teachers to create engaging technology-assisted learning experiences for their charges. One of the features that many science and math teachers find useful is the ability to create links ...

 GeoGebra link: https://www.geogebra.org/m/hscshcj8 This simulation demonstrates the power dissipated in a variable resistor given that the battery has an internal resistance (made variable in this app as well). Since the power dissipated by the resistor is given by and the current is given by , This power will be a maximum if the expression for the denominator is a ...

Some of the more challenging problems in the topic of electricity in the A-level syllabus are those involving a potentiometer. The solution involves the concept of potential divider and the setup can be used to measure emf or potential difference across a variety of circuits components. Basically, students need to understand the rule – that ...

I’ve curated a series of Geogebra apps that are relevant and useful for the instructional objectives under the Singapore-Cambridge GCE ‘O’ and ‘A’ level syllabi. Some of these apps were created by myself. If you have any ideas for new Geogebra apps, do let me know in the comments section below and I’ll see if ...

 GeoGebra link: https://www.geogebra.org/m/ev62ku7w Students can explore how varying frequency and amplitude of the vertical oscillation of a platform could cause an object resting on it to temporarily leave the platform (i.e. when normal contact force is zero).

 GeoGebra link: https://www.geogebra.org/m/xyqhfvyw Applying the 1st Law of Thermodynamics to 4 simple changes on an ideal gas, students can check their understanding using this Geogebra app. When is work done positive? Which processes bring about an increase in internal energy or temperature? Which processes require heat input?

As one of the first topics in A-level physics, kinematics introduces JC students to the variation of velocity and displacement with acceleration. Very often, they struggle with the graphical representations of the 3 variables. This Geogebra app allows students to vary acceleration (keeping it to a linear function for simplicity) while observing changes to velocity and ...

GeoGebra link: https://www.geogebra.org/m/hzfyjejx GeoGebra link: https://www.geogebra.org/m/jmqytcsc

In order to help students visualise a wavefront, a 3-D image is usually used to show the imaginary line joining particles in phase. I created the Geogebra apps below to allow students to change the wavefront and observe it move with time at a constant wave speed. There represent simplified versions of waves on a ...

 GeoGebra link: https://www.geogebra.org/m/f7faw3r6 This simple Geogebra app allows students to observe the oscillation of a particle perpendicular to the direction of energy transfer.

This Geogebra app allows students to explore how the position of the centre of gravity as well as the width of its base affect the stability of an object.

 This animation is made using Geogebra. It shows the instantaneous velocity and displacement vectors of a particle undergoing simple harmonic motion while tracing its position on the velocity-displacement graph. It is meant to help student understand why the graph is an ellipse.