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.

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:

]]>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.

]]>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 SLS – a wonderful tool to have during this period of full home-based learning.

]]>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 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.

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

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

- Make the two strings exerting the downward tensions 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.
- The two strings should be sufficiently far apart to prevent the floating structure from tilting too easily to the side.
- The centre of gravity of the floating structure must be in front of the string exerting the upward tension.
- The base must be big enough to prevent the whole structure from toppling.

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

]]>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 sine rule or the cosine rule to solve for magnitudes of forces instead of scale drawing, which is often unreliable.

For students who are not familiar with these rules, here is a simple summary:

If you are trying to find the length of a side while knowing only two angles and one side, use sine rule:

$$\dfrac{A}{\sin{a}}=\dfrac{B}{\sin{b}}$$

If you are trying to find the length of a side while knowing only one angle and two sides, use cosine rule:

$$A^2 = B^2 + C^2 – 2BC\cos{a}$$

]]>Which vector triangle represents the forces on the ladder?

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