Seng Kwang Tan

Unequal masses attached to rod in free fall

Came across a question recently that many students answered incorrectly.

Close to the surface of the Earth the gravitational field strength is uniform. A pair of unequal masses are joined by a light, rigid horizontal bar and suspended by a string from their centre of gravity as shown. The mass M of the ball on the left is larger than the mass m of the ball on the right.

The supporting string is now cut and the system begins to fall. Air resistance is negligible.

Which statement is correct?

AThe bar will remain horizontal as it falls.
BThe bar will rotate clockwise as it falls.
CThe bar will rotate anti-clockwise as it falls.
DThe bar will first rotate clockwise and then rotate anticlockwise as it falls.

Without air resistance

This question supposes that air resistance is negligible and so the only forces initially acting on the object is weight. The answer that many students gave incorrectly as B because they assume that the larger weight acting on the larger mass will bring about a larger acceleration.

Since the object begins in equilibrium, and the acceleration of both objects is just gravitational acceleration, the bar will remain horizontal.

With air resistance

This then invites a question: What if there is air resistance?

To consider the vertical acceleration on both balls, we need to consider the net force $F_{net}$, which is the vector sum of weight $W$ and air resistance $F_R$, ignoring the tension exerted by the rod at the initial stage of the fall.

$$F_{net} = W – F_R = V \rho_{ball}g – \dfrac{1}{2} \rho_{air}v^2C_DA$$

The volume V of a sphere is proportional to $r^3$ and its cross-sectional area A is proportional to $r^2$,

A larger radius will imply a larger increase in V than A, and hence, a large $W$ than $F_R$. This will then allow the larger mass to experience a larger acceleration than the smaller mass in the initial stage.

Internal Resistance and Terminal Potential Difference

This applet demonstrates how terminal potential difference (as measured by the voltmeter across the terminals of the battery) changes depending on :

  1. internal resistance r
  2. external resistance R
  3. emf E
  4. when a switch is turned on and off
<iframe scrolling="no" title="Internal Resistance and Terminal Potential Difference" src="" width="640px" height="480px" style="border:0px;"> </iframe>

Man in Elevator

I just took the elevator in my apartment building with the PhyPhox mobile app and recorded the acceleration in the z-direction as the lift went down and up. This was done in the middle of the night to reduce the chances of my neighbours getting into the elevator along the way and disrupting this experiment, and more importantly, thinking I was crazy. The YouTube video below is the result of this impromptu experiment and I intend to use it in class tomorrow.

I used to do this experiment with a weighing scale, and a datalogger, but with smartphone apps being able to demonstrate the same phenomenon, it was worth a try.

To complement the activity, I will be using this simulation as well. Best viewed in original format:, this simulation done in 2016 was used to connect the changes in acceleration and velocity to the changes in normal contact force as an elevator makes its way up or down a building.

Sky-Diving and Terminal Velocity

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 have changed the default values of the terminal velocities to match those of the video below for consistency.

Also relevant is the following javascript simulation that I made in 2016 which can show the changes in displacement, velocity and acceleration throughout the drop.

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 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
  2. Evan’s Space (for O-level students) – by Edgefield Secondary School teacher, Evan Toh at
  3. The Physics Grove (for O-level students) – by Hillgrove Secondary School teacher, Jonathan Ho at
  4. Open Educational Resources (for all students) – by Senior Specialist, Lawrence Wee at

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.