### Thinking [email protected] #2

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by Aaron. More of him can be found here.

Assuming an object is moving in a circular motion in a polar coordinate system given by $x = r \text{cos} \theta$ and $y = r \text{sin} \theta$. Can you derive the formula of the centripetal acceleration? Hint: look at one of the axes and think of the direction and what is centripetal acceleration

### Thinking [email protected] #1

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by Aaron. More of him can be found here.

Kepler’s Third Law states that the period of a planet’s orbit is directly proportional to the cube of the semi-major axis of its orbit. This allows scientists to calculate distances of planets in our solar system. Can you derive the equation using what you have learned in Motion in a Circle and Gravitational Field?

### [email protected] #1

[email protected] is a series of questions that we, as tutors feel that are useful in helping students think and improve their understanding.

Thinking [email protected] is curated by Aaron. More of him can be found here.

Why study Physics?

I have questioned many students and getting answers ranging from “Just a subject that I have to take in A-Level” to “I do not know what else to take?”

It is not just a subject:

Physics can be seen as a ‘tool’ to enable you to be more logical and you practise and learn to question ‘Why’, which is an invaluable asset to many other jobs or careers

A student’s dad was having a good chat with me and he was a control systems engineer back in his younger years in The States for a good decade or so. Thereafter he went on to take an MBA and he is now an MD in a local bank. Even if you are not going to major in engineering, it can be a good training.

Helping out with the house:

You can of course repair and fix things in the house without studying Physics but if you know more about topics like pressure, forces, electricity and how things work, won’t it be awesome that you are more knowledgeable? It can be a general knowledge and it will help you out in life along the way when things are screwed at home.

It puts your maths to good use:

Lots of formulas? Well, they help physicists and engineers to understand the world we live in.

Becoming an Engineer:

It is a myth that only bankers are being paid well. Only the good bankers are well paid, similar to engineers. If you excel in the things you do, you will be rewarded. Engineers are not technicians. Yes, they can fix things but they innovate and SOLVE problems too.

A world without Physics:

You will not be looking at this now on your computer/laptop or mobile device literally. Engineers continuously apply Physics to push the frontiers of technology.

It is not just a subject:

Physics can be seen as a ‘tool’ to enable you to be more logical and you practise and learn to question ‘Why’, which is an invaluable asset to many other jobs or careers

A student’s dad was having a good chat with me and he was a control systems engineer back in his younger years in The States for a good decade or so. Thereafter he went on to take an MBA and he is now an MD in a local bank. Even if you are not going to major in engineering, it can be a good training.

Helping out with the house:

You can of course repair and fix things in the house without studying Physics but if you know more about topics like pressure, forces, electricity and how things work, won’t it be awesome that you are more knowledgeable? It can be a general knowledge and it will help you out in life along the way when things are screwed at home.

It puts your maths to good use:

Lots of formulas? Well, they help physicists and engineers to understand the world we live in.

Becoming an Engineer:

It is a myth that only bankers are being paid well. Only the good bankers are well paid, similar to engineers. If you excel in the things you do, you will be rewarded. Engineers are not technicians. Yes, they can fix things but they innovate and SOLVE problems too.

A world without Physics:

You will not be looking at this now on your computer/laptop or mobile device literally. Engineers continuously apply Physics to push the frontiers of technology.

### Meritocracy? Junior colleges merger and its implications

It’s pretty interesting that shortly after our post on meritocracy, we have news about the junior college (JC) mergers. For more information about the news, you could take a look at this weblink.

This drastic move by MOE has sparked a lot of concerns among the public and has brought up a few issues for us to consider. First, it would be the falling demographics of Singapore. The falling birth rates is cited as the main reason for the merger of schools, so that resources would not be wasted, and there would not be under-utilized staff in the system. With such falling birth rates, what would you think is going to happen to the future of the educational landscape (would teaching/tutoring as a profession still be lucrative? We know that MOE has cut back on the hiring of teachers from 3000 at its peak yearly to about 1000 right now).

Second question to think about would be the larger implications of these schools merger. Why are these schools selected? Some have argued that it is a strategic move by the government to level the playing field by merging these colleges so that academic standards would be streamlined? of course, we cannot merge schools like RI and HCI together as it would only further consolidate their super-elite status in society (besides strong school culture and powerful alumni).

Finally, school culture and history is being destroyed when merger takes place. If that’s the case, what does it say about how the nation values history? It is all about the future and progress right, the past no longer matters if it is holding us back. Pragmatism is the view of the Singapore’s state.

### Probability Question #4

A gambler bets on one of the integers from 1 to 6. Three fair dice are then rolled. If the gambler’s number appears $k$ times ($k = 1, 2, 3$), he wins $$k$. If his number fails to appear, he loses$1. Calculate the gambler’s expected winnings

### Evaluation for Application Question (AQ)

Have you ever wonder what teachers mean by evaluation? Many students have asked me this during my classes.

Well to put it simply, evaluation for the AQ is not just simply stating whether you agree or disagree. You would need to provide a reason to support your point. So how exactly should you evaluate? Well you can consider commenting on the limitations or applicability of the author’s point or even how persuasive/convincing the author is in bringing across his point of view.

Here are some tricks that you could possibly use to help you in your evaluation to make it SUPER:

S– Span (whether the argument applies only to the past and not the present day context and vice versa)

U– Underlying assumption of the author

P– Perfect world vs Reality (does the argument exist only in theory/ in a perfect world, but not applicable in reality?)

E– Effectiveness of the argument

R– Reach (what are the different demographic groups which this argument applies to? surely it can’t apply to all?)

Using this framework, I’m sure you would be able to impress your tutors with your AQ from now on!

### Characteristics of Singapore’s society (Application Question)

This list is non-exhaustive and serves as a guide for you to expand on Singapore’s characteristics…  Pls take a look at my previous post on Singapore’s characteristics, so that you would have a better overview.

1. Highly globalized and connected city, with heavy focus on technological developments
2. Highly educated
3. High cost of living
4. Pragmatic, concerns usually surround economic issues and survivals
5. Low birth rate
6. Greying population
7. Highly affluent- high levels of disposable income
8. Migrant society with identity in constant flux
9. Long working hours (one of the highest in the world) rat-race pace of life
10. Religious/ racial harmony
11. Apathetic
12. Capital and knowledge-intensive economy
13. High levels of censorship by the government
14. Conservative

When writing your AQ, you should always try to input these into your paragraphs to demonstrate an awareness of Singapore’s society and to show the relevance of the argument to Singapore.

### A little reminder to students doing Calculus now

When $\frac{dy}{dx} = 0$, it implies we have a stationary point.

To determine the nature of the stationary point, we can do either the first derivative test or the second derivative.

The first derivative test:

Students should write the actual values of $\alpha^-, \alpha, \alpha^+$ and $\frac{dy}{dx}$ in the table.

We use this under these two situations:
1. $\frac{d^2y}{dx^2}$ is difficult to solve for, that is, $\frac{dy}{dx}$ is tough to be differentiated
2. $\frac{d^2y}{dx^2} = 0$

The second derivative test:

Other things students should take note is concavity and drawing of the derivative graph.

### Vectors Question #2

If $c = |a| b + |b| a$, where $a$ , $b$ and $c$ are all non-zero vectors, show that $c$ bisects the angle between $a$ and $b$.

### In times of economic hardship, should a country still be expected to provide financial or material aid to others?

Students are expected to address the criteria of this question throughout the essay; it being in times of economic hardship. For a quality essay, the terms “should” and “expected” should be addressed as well. For instance, a country should still give aid, but perhaps not be expected at a time when its survival is in question, and it does not have a healthy budget balance.

Financial aid- capital/loans/money

Material aid- manpower/distribution of basic goods and necessities

• Provision of aid during economic hard times could be a political statement and commitment to the recipient country, helping to foster greater political relations in the long term. Giving of aid should be expected especially if the recipient country needs it more than the donor country. Such circumstances could be when the recipient country is facing civil war and there is urgent need of aid to cease the fighting etc. Another possible instance could be during times of natural disasters/emergencies. Also, for most of the donor country, aid takes up a small portion of their budget, hence it should not affect the current economy severely even if the country continues to give out aid during hard times. Aid accounts for 0.5% of the US budget yearly.
• Governments should be responsible and accountable to their citizens first especially during hard times, hence aid should be allocated domestically rather than elsewhere. The dollar votes of the citizens and their voices are important, and it is only right that countries should be concerned with their own self-preservation before others. After all, an economically prosperous country will then be able to contribute more to the international community, rather than a slow and stagnate economy that is facing difficult times.
• Perhaps a country should look at other means of support, rather than the provision of aid during bad times. It is presumptuous to assume that aid helps to alleviate the problems faced by the recipient countries. Often, aid may actually harm local industries and foster this sense of self-entitlement and dependency on the donor nations.
• Legal obligations under international law could possibly bind countries to continue giving aid to another country. A short term economic difficulty does not suffice to repudiate this commitment, especially when contracts have been signed beforehand, and the donor country may risk ruining their legitimacy and international standing.

In dire situations, countries should still continue to give aid to one another. However, expectations to scale down in terms of aid is definitely reasonable and justifiable.