the world in a different light
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 by varying r and ω.
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 arc equal in length to its radius.
Mathematics defines the constant π as the ratio of a circle’s circumference to its diameter. This can also be shown in the app, although you need to drag the moving point to a point just short of one full revolution.
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 the pdf document above and make a simple interactive applet yourself too. The outcome of the interactive applet will be like this:
The following instructions are added on 19 Nov 2024 to update the screens available in SLS.
To embed a GeoGebra app into the Singapore Student Learning Space or any other LMS that supports iframe embedding, note the following:
The size of the interactive should be able to fit a mobile device. I suggest 640px width and 480px height for interactives meant for the Singapore Student Learning Space (SLS). To change the dimensions, go to the page of the specific interactive you want to embed and click on the “more” button (3 dots in a vertical row). Click on “Edit Activity” as shown below.
Next, click on the pencil icon to show “Advanced Settings”
Edit the width and height as required.
Click “Done” and “Save”
To get the embedding codes, go to the “more button” again (see above) and select “Details”.
Click on “Share” and select the “</>Embed” tab.
Copy the iframe embed code and paste it into SLS or your preferred LMS.
In SLS, select “Text/Media” and “Website” to insert the code.
I am taking the opportunity (since my students are all doing home-based learning) to teach them how to use spreadsheets to do calculations and to obtain a best-fit line. While they can still submit graph work using PDF scanning apps such as Office Lens and Camscanner into Google Classroom for me to mark, they can make use of the spreadsheet-generated graph to check their results.
Even though for exams, we still require them to plot the points on paper and obtain the gradient and intercept from points on the best-fit line, nobody is going to do so when they start working. So I might as well teach them now.
Due to the lack of face-to-face time, I made this step-by-step video showing them how to do so.
For lab work, students often have to estimate a line of best fit for their data points manually. It takes a bit of practice to get it right. With this app, students can generate data points with varying types of scatter and predict their own best-fit line before comparing it with a computer generated one based on the least mean square method.
This simulation can be used for O-level Physics, for the topic of Pressure. I created it as it was relevant to our school’s IP3 physics as well.
It demonstrates the working principle of a hydraulic press. By adjusting the cross-section areas (A) of the two cylinders, you only need a small amount of force at the narrow piston to exert a large amount of force at the wider piston. This is how, when driving, the force applied by one’s foot is enough to supply a large force to apply the brake pads on a car’s wheels.
The advantage of using GeoGebra is that one can create such simple simulations within a couple of hours and it can be readily embedded into Google Classroom, Microsoft OneNote, SLS – a wonderful tool to have during this period of full home-based learning.