A-level Topics

09 May

Fleming’s left-hand rule vs right-hand palm rule

Seng Kwang Tan 16 Electromagnetism 0 Comments

Fleming’s Left-Hand Rule and the Right-Hand Palm Rule are visual tools used to predict directions in electromagnetic interactions.

Fleming’s Left-Hand Rule applies to electric motors and helps determine the direction of the force (motion) on a current-carrying conductor placed in a magnetic field. By aligning the thumb (force, $F$), first finger (magnetic field, $B$), and second finger (current, $I$) at right angles, one can deduce the force direction.

The Right-Hand Palm Rule serves the same purpose, but might actually be more intuitive, as the fingers would look like parallel vectors in a uniform magnetic field. The thumb points in the direction of the current. The hand will then naturally look like it is exerting a push in the direction of the palm.

I like to joke with my class that both serve the same purpose but one resembles a gun while the other resembles a kungfu move. Which would you prefer?

Side note: The image above is generated using a single prompt with ChatGPT 4o: “draw an image representing fleming’s left hand rule, next to the right-hand palm rule.” I’m impressed by how far AI image generation has come.

05 April

Simulation of Projectile Motion with Air Resistance

Seng Kwang Tan 02 Kinematics, 03 Dynamics, IP3 03 Dynamics, Simulations 0 Comments
Open in new tab 🔗 This simulation offers a hands-on and dynamic way to explore the physics of projectile motion with and without air resistance. By adjusting parameters such as launch velocity, angle, and air resistance, users can visualize how these factors affect the shape and reach of a projectile’s trajectory. The app provides real-time changes including motion paths, velocity vectors, and a velocity-time graph showing horizontal and vertical components separately. It also calculates and displays key quantities such as maximum height and range under ideal and non-ideal conditions (based on an arbitrary coefficient of drag. Through interactive experimentation and visual reinforcement, learners gain a deeper understanding of concepts the effect of air resistance, and the difference between theoretical and real-world motion. This is suitable for JC1’s topic on projectile motion. It can also be used for Upper Sec, if you change the launch angle to 90 degrees.
15 March

Interactive System Schema Generator

Seng Kwang Tan 03 Dynamics, IP3 03 Dynamics, Simulations, Student Learning Space 0 Comments

I built this web app to help students draw system schemas, having blogged about this before.

It is also available and optimised for download for SLS.

Basic Instructions

To add Bodies:

  • Click the “Add Body” button.​
  • Click on the canvas to place the body at your desired location.​
  • Label the Body.

Add Forces:

  • Click the “Add Force” button.​
  • Click on two bodies that exert the force on each other.​
  • Label the Force.

Using System Schema to Understand Newton’s Third Law

Newton’s Third Law states that when Body A exerts a force on Body B, Body B exerts an equal and opposite force on Body A. While this principle is conceptually simple, many students struggle to apply it consistently across different physical scenarios. The System Schema approach provides a powerful way to visualise and analyse these interactions. It is a representation tool developed by The Modeling Instruction program at Arizona State University (Hinrichs, 2004).

A system schema is a diagram that represents objects (as circles) and interactions (as lines) between them. Instead of focusing on individual forces, a system schema helps students see the relationships between objects before applying force diagrams. This method emphasizes Newton’s Third Law by explicitly showing how forces come in pairs between interacting objects.

To correctly identify action-reaction force pairs, consider the following guidelines:​

  1. Forces Act on Different Objects: Each force in the pair acts on a different object. For example, if Body A exerts a force on Body B, then Body B simultaneously exerts an equal and opposite force on Body A.​
  2. Forces Are Equal in Magnitude and Opposite in Direction: The magnitudes of the two forces are identical, but their directions are opposite.​
  3. Forces Are of the Same Type: Both forces in the pair are of the same nature, such as gravitational, electromagnetic, or contact forces.

The steps to applying System Schema to Newton’s Third Law are as follow:

  1. Identify the bodies in the system – Draw each object as a separate circle.
  2. Represent interactions – Draw lines between bodies to indicate forces they exert on each other (e.g., a box on the ground interacts with Earth through gravitational force).
  3. Label force pairs – Each interaction represents an action-reaction force pair (e.g., a hand pushes a wall; the wall pushes back).
  4. By mapping forces this way, students can easily recognize that forces always act between bodies and in pairs, reinforcing the symmetry of Newton’s Third Law.

One of the most common misconceptions of students is that normal contact force and gravitational force acting on a body are action-reaction pairs because they are equal and opposite in a non-accelerating system. By using the system schema, they can see that the two forces involve interaction with different bodies, e.g. the floor of an elevator for normal contact force, and the Earth for gravitational force.

25 September

Turning Effect due to Non-Perpendicular Forces

Seng Kwang Tan 04 Forces, IP3 04 Forces 0 Comments

When applying the principle of moments to calculate the magnitude of a force creating a turning effect, where the force is not perpendicular to the length of the object, there are two approaches.

Take the following problem:

A uniform rectangular beam has negligible thickness and weight 850 N. Its length is 5.0 m and it is in contact with the top of a support at point P. P is 0.80 m from one end of the beam.

The beam is held stationary, at an angle of 30° to the horizontal, by a rope that is attached to the bottom corner of the other end of the beam.

Calculate the magnitude of the force T on the beam due to the tension in the rope.

Approach 1: Identifying the perpendicular distance between line of action of the force and pivot

In the applet above, check the box that says “Show perp dist” to see the lines representing the perpendicular distances between each line of action of the force and the pivot P.

Taking moments about P,

Clockwise moment due to T = Anti-clockwise moment due to W

$$T \times (5.0\text{ m} – 0.8\text{ m}) \sin 30^{\circ} = W \times (\dfrac{5.0\text{ m}}{2} – 0.8\text{ m}) \cos 30^{\circ}$$

$$T \times 2.10 \text{ m} = 850 \text{ N} \times 1.472 \text{ m}$$

$$T = 596 \approx 600 \text{ N}$$

Approach 2: Resolving the forces to obtain components of forces perpendicular to the beam

In the same applet, check the box that says “Resolve forces”

Taking moments about P,

Clockwise moment due to $T_{\perp}$ = Anti-clockwise moment due to $W_{\perp}$

$$T \sin 30^{\circ} \times (5.0\text{ m} – 0.8\text{ m}) = 850 \text{ N} \cos 30^{\circ} \times (\dfrac{5.0\text{ m}}{2} – 0.8\text{ m})$$

$$T \times 0.500 \times 4.2 \text{ m} = 850 \text{ N} \times 0.866 \times 1.7 \text{ m}$$

$$T = 596 \approx 600 \text{ N}$$

04 August

Interactive Graph with Javascript

Seng Kwang Tan 02 Kinematics, AI, IP3 02 Kinematics 0 Comments

I was experimenting with using generative AI to create an interactive graph that could be used to amend the animation of a moving particle, for the topic of kinematics. Students are able to move the four points on the velocity time graph to manipulate the movement. I kept the graph to straight lines between each point to keep things simple.

The vertical axis toggles between displacement and velocity. This will be yet another way for students to learn about how the velocity-time graph affects motion. I have found that many students are confused between displacement and velocity. The app’s ability for them to vary the velocity graph and then make predictions of the resulting displacement graph and the movement should be worth the effort.

02 July

Random displacement and velocity simulation

Seng Kwang Tan 02 Kinematics, IP3 02 Kinematics 0 Comments

Oftentimes, the kinematics graphs that students see in their textbooks are very clean and simple. In nature, movement is often haphazard and to simulate such movement in one dimension, I generated this (https://physicstjc.github.io/sls/random-displacement/index.html) using ChatGPT 4o.

There is a drop-down menu that allows users to toggle between displacement and velocity graphs.

In a displacement-time graph, the displacement is plotted on the y-axis and time on the x-axis. A positive displacement represents a position to the right of the origin while a negative displacement is to its left. The slope of this graph represents the object’s velocity; a steeper slope indicates a higher velocity. A positive slope means the object is moving forward, a negative slope indicates it is moving backward, and a zero slope shows the object is at rest. For example, in uniform motion, the displacement-time graph is a straight line with a constant slope, reflecting constant velocity.

Conversely, in a velocity-time graph, velocity is on the y-axis and time on the x-axis. The area under the velocity-time graph represents the object’s displacement. Areas above the time axis denote positive displacement, while areas below indicate negative displacement.