I have three goals for this article on HSC Physics Formulae:

- I want you to be able to recognise formulae.
- I want you to be able to interpret formulae.
- I want you to know how to use them!

I also have three statements to make as to why this isn’t an article about how to *memorise* HSC Physics Formulae, but how to *understand *them:

- If you memorise a formula without understanding it, you are wasting your time.
- If you do not understand a formula, you cannot apply it to a question.
- If you cannot apply the correct formula to a question, you will not get the correct answer and will lose marks.

Let’s not beat around the bush – let’s get started!

## What are all the formulae I need to know?

### Grab the formula sheet, syllabus, and your textbook of choice

You can grab a copy of the formula sheet here.

You can get the HSC Physics Syllabus here.

As for the textbook, I would personally recommend Physics in Focus.

The equations in the textbook are highlighted and all terms explained, making them easy to find and understand. Often there are examples right after a formula is introduced, so you can see how it is used.

### Now it’s time to identify formulae that aren’t given to you!

Whilst there is an extremely helpful formula sheet in HSC Physics, there are a few formulae that are missing. (*Hint: Orbital velocity is one such formula that is missing, are there any others?*)

Action Point!Go through the textbook page by page, tick off the formulae on the formula sheet as you find them. I assure you however, there are some missing, your task is to find every one and write it down.

### When are you likely to use the formula in an exam?

Once you’ve identified all the formulae you need, it’s time to identify when you’re going to need each one! I could have asked you to do this whilst you were going through the textbook and had the topic in front of you however I did it this way because I want it to be a memory challenge; **can you identify where each formula came from? **

**This is a good way to do a quick audit.** If you’ve prepared well and read the textbook closely, you should remember!

If not that’s okay, this can be an eye opening experience on the difference between actually actively paying attention whilst reading and merely skimming.

With enough exposure to problems, and enough reference back to the formulae, the chances are you’ll remember most of them and there will only be a few you’re unsure of. Just go back over those ones until you feel certain about which topics formulae belong to.

We’re intentionally going in baby steps – you don’t have to be 100% confident with EVERY formula, nor do I expect you to have memorised all the formulae. All I want is for you to be sure which topic the formulae come from.

Now that you know which topics the formulas come from, let’s try and start really understanding them!

## What is the formula telling me?

### ASK YOURSELF: What are the terms in the equation?

This should be the first question you ask yourself when you look at a formula,** do you know what all the terms are?**

Let’s consider the orbital velocity equation from earlier: what is the mass in the equation? Is it the mass of the orbiting body, or the mass of the planet that is being orbited?

It’s the mass of the planet being orbited!

I think it is important to appreciate not only what is in the equation but what isn’t!

This might sound bizarre, but consider the equation for orbital velocity again, notice the mass of the orbiting body is not involved. That means regardless of whether a feather is orbiting the Earth or whether it is the moon, provided they are orbiting at the same radius they will be going at the same speed! That’s some powerful stuff, and all that information is contained in one equation.

### ASK YOURSELF: Where do the formulas come from?

We’ve talked so much about orbital velocity we may as well continue. Do you know where it comes from?

Remember that to keep a body moving in a circle we require a centripetal force. i.e.

We also know this force must be caused by gravity since gravity is a central force, and there are no other forces at play. i.e.

**Try and understand where the formulae you use come from**.

You won’t need to derive them all in an exam, but knowing where they come from can help. Going through a derivation like the one above for the different formulae you come across can give you a deep insight into the physics behind a phenomenon.

### ASK YOURSELF: What are the units?

**Make sure you know the units in your equations.**

For example, in the equation above it is assumed, the mass and radial distance are measured in Kilograms and metres respectively. The resultant velocity you get from your calculation should be in metres per second. The units must match! Why is that?

The reason everything must be in metres and kilograms in this calculation is actually because of the way the gravitational constant has been defined. You’ll notice the Board of Studies has defined the constant in terms of SI units. (As they should! In 1999 NASA lost about 125 million dollars because they stuffed around with their units and things didn’t match! It goes to show even the best of us can make mistakes so be careful!)

What we have stumbled across here is dimensional analysis, and it is incredibly powerful! Real world physicists use it every day to make sure their theoretical predictions make sense. We can use it to check equations make sense, it is just a fancy word for making sure units’ match! Let’s see it in action.

Consider Newton’s law of universal gravitation:

Let’s rearrange for G:

If we look at the units we have on the right hand side, we know the gravitational constant must have the same units:

Which you’ll find matches the formula sheet exactly!

## Ok… I know the formula, how do I use it?

### You should now know what the terms are in the equation, can you identify them in specific questions?

Which equation should we use in the question below?

The question says: *“An electric field is produced between two charged plates”*. There is only one equation we know involving charged plates and electric fields, it must be:

Ask yourself what you are being asked to solve for? In this case it is V, so we better rearrange our equation.

At this point I would like to intentionally make a mistake in the hope that you won’t make it as well! We will use our trick from earlier (Dimensional analysis) to catch the mistake. We are told the strength of the electric field, E as well as the separation distance d. So let’s substitute in!

Notice the units of metres and centimetres wont cancel! We need to change to metres.

Much better! This is probably not the first time you’ve heard that your units must be in SI units, this has probably been drilled into you from your teachers, but hopefully you now appreciate just why we do it, we need the units to match!

### Substitute as late as possible! Use your calculator wisely!

Notice I didn’t substitute until the very end: **always try and rearrange your equations and substitute as late as possible. **

Numbers in physics are usually incredibly large or incomprehensibly small! Typing them into your calculator can be a nightmare, not to mention prone to error, so try and do this as late as possible. Think twice type once!

Another thing worth mentioning now is **using your calculator to its full potential**. If you didn’t know already, you can store numbers in your calculator! This is incredibly useful in physics because of these ugly big and small numbers. It can make typing them easier, so you can fit more of the calculation on the screen easier, and it makes the chance of error a lot smaller!

I know a favourite among HSC students is the Casio FX-82AU Plus – it is one of the most common calculators. If you have a different calculator, you should be able to find out how to store numbers in the user manual. Most of you however will have the calculator in the picture below.

Here’s the procedure to store a number if you have a Casio:

For this example, let’s store the speed of light into our calculator so we don’t have to type it out every time!

- Just type 3*10^8 into your calculator and press “=”
- Now press “SHIFT” and then “RCL” you will see the letter “STO” above the key, this allows us to store a number. I’ve circled it in red, in the picture above.
- Now we will pick the letter we want to store it into. (I recommend C, since it is consistent with the convention in physics.) To store it in the letter “C”, just press “HYP” (you DO NOT need to press “ALPHA” before choosing the letter you want.)

When you want to use the speed of light next time you won’t have to type it out just use “C”. To use “C” just hit “ALPHA” and then “HYP”.

This can be confusing the first time, so you should practice. Try storing the fundamental charge, or the electron volt in the letter “E”.

- Remember when storing you DON’T need to press ”ALPHA”
- When you want to use a letter you’ve stored you DO need to press “ALPHA”

## Committing the formulae to memory and general tips!

I left this until last for good reason. **It is very difficult to remember something when you don’t understand it, more importantly I’d argue it’s pointless.** That’s why we spent this time to make sure you really understand all these formulae, now memorising them shouldn’t be too difficult.

To those of you who struggle with remembering formulae, I wouldn’t worry too much, most of them are on the formula sheet! If you’ve followed the steps above and have identified the ones that aren’t on the sheet, you only really have to memorise those!

If you’ve looked through the derivation and where a formula comes from, you should be able to re-derive it in an exam if need be. If you can’t remember, there is always our good friend dimensional analysis which can give you an idea of if you’re on the right track. Please write out the formulae by hand, this can make a huge difference, and make sure you use them too, do some questions!

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## Good Luck!

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**Vamsi Srinivasan** is looking to uncover the next hidden truth of the universe. He was so fascinated by the beauty of Physics and Mathematics during his HSC that he went on to study Physics at University. He is now in his second year of a dual degree in Physics/Computer Science. He loves physics and maths so much, he wanted to share his passion and has been an Art of Smart coach for the past 2 years. He’s helped coach students in physics as well as all ranges of HSC Maths from General to Extension 2. In his spare time you can find him watching Tennis or Formula 1 or perhaps listening to his favourite podcast ‘Hello Internet’.