  # 1.3. Vectors and Scalars

This section is pretty much fundamental to what comes later in the IB Physics course. Physics is all based around the idea of 'measuring stuff'. The 'stuff' we measure - such as time, mass, temperature are what are known in Physics as quantities. We can characterise each of these quantities as either a Vector or a Scalar. You need to understand the key differences between the two, but the main focus on this chapter is building in a bit of your GCSE Maths (your Trigonometry and Pythagoras) to apply to lots of tricky Mechanics problems. It's worth getting some practice in here early on - this stuff gets used a lot.

Clearly, the idea of vectors is important in navigation. In order to move from A to B, I need to know both how far to move as well as in what direction. If you have ever planned an outdoor hiking expedition, this involves plotting a number of individual distances and compass bearings along various checkpoints- this is actually a series of displacement vectors. Before diving further into this subject, it feels necessary to show this little clip from the movie 'Airplane', with the famous line, "What's our Vector, Victor?"... just because I can.

I break the topic down as follows:

#### What are Vectors and Scalars?

The quantities that we measure in Physics fall into one of the two categories. Scalars are nice and simple to understand as they only have a magnitude (number) associated with them. Vectors involve some more complex Maths as we need to consider their direction too.

You previously looked at this at GCSE. If the basics are a little rusty take a look at this nice video by Cognito to refresh your memory.

Before diving into the mathematics of vectors, it's worth putting this into a bit of context. You may have previously looked at a little bit of vector mathematics in maths lessons previously. The vector quantities we have looked at (e.g. displacement, force, acceleration) all follow the rules of vector maths - i.e. we can add them together, subtract them, or resolve them into components.

There is a nice TedEd video on vectors below - the notation used is a little mathematical, but it is a nice introduction to the section.

## Video Lessons

 Khan Academy Introduction to Vectors & Scalars Physics Online Vectors and Scalars Arrow Notation Study Nova Introduction to Vectors 1 Introduction to Vectors 2 Vectors vs Scalars 1 Vectors vs Scalars 2

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Isaac Physics Describing Vectors Mr. G 1.3 Teaching Notes 1.3 Student Notes

## Questions

 Grade Gorilla 1.3 (Vectors & Scalars) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Mr. G 1.3 Formative Assessment Topic 1 Summary Qs IB Specific Questions Physics and Maths Tutor Scalars & Vectors (AQA 2) Scalars & Vectors MS (AQA 2) A-Level Qs: overlapping content Physics and Maths Tutor Nature of Quantities 1 (OCR) Nature of Quantities 1 MS (OCR) Nature of Quantities 2 (OCR) Nature of Quantities 2 MS (OCR) A-Level Qs: overlapping content

#### Resolving Vectors

Resolving a vector means splitting it up into two different perpendicular components (i.e. I take a diagonal arrow, and split it up into an equivalent vertical and horizontal arrow). This is very useful in Physics but requires a little bit of Geometry. To the left I have the red vector 'a' (the line above represents the fact it is a vector) - this could be a displacement showing a movement in a certain direction for example.

To resolve 'a' I want to split it into its horizontal and vertical components which are shown in white. If this were a displacement , my white components 'ax' and 'ay' would these would be how far right and how far forward I've moved from my starting point respectively.

## Video Lessons

 Khan Academy Breaking vectors into components Physics Online Resolving Vectors Science Shorts Easy Resolving Vectors Trick Study Nova Notation 1 Notation 2 Examples 1 Examples 2

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Isaac Physics Resolving Vectors Mr. G 1.3 Teaching Notes 1.3 Student Notes

## Questions

 Grade Gorilla 1.3 (Vectors & Scalars) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Components of a Vector Mr. G 1.3 Formative Assessment Topic 1 Summary Qs IB Specific Questions Physics and Maths Tutor Scalars & Vectors (AQA 2) Scalars & Vectors MS (AQA 2) A-Level Qs: overlapping content Physics and Maths Tutor Nature of Quantities 1 (OCR) Nature of Quantities 1 MS (OCR) Nature of Quantities 2 (OCR) Nature of Quantities 2 MS (OCR) A-Level Qs: overlapping content

Vector addition is very useful in a number of circumstances. If I have lots of forces acting on an object, adding together the individual vectors will tell me the resultant force acting on the object. If If I swim across a river at a certain velocity, and the river is flowing perpendicularly at another velocity, the vector sum of these velocities will tell me the overall speed and direction in which I'll be moving. Vector addition is very useful in finding the resultant of multiple vectors (e.g. momentum, force, displacement).

Make sure you have had a bit of practice resolving a vector into it's constituent components before tackling this section - addition builds upon those basics, but involves the same principle mathematical ideas.

The Physics Classroom have a nice little walkthrough section about vector geometry.

## Video Lessons

 Khan Academy Visualising Vectors in 2D Adding and Subtracting Vectors Physics Online Adding Vectors Study Nova Addition of Vectors

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Isaac Physics Vector Addition Mr. G 1.3 Teaching Notes 1.3 Student Notes

## Questions

 Grade Gorilla 1.3 (Vectors & Scalars) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Isaac Physics Adding Vectors Mr. G 1.3 Formative Assessment Topic 1 Summary Qs IB Specific Questions Physics and Maths Tutor Scalars & Vectors (AQA 2) Scalars & Vectors MS (AQA 2) A-Level Qs: overlapping content Physics and Maths Tutor Nature of Quantities 1 (OCR) Nature of Quantities 1 MS (OCR) Nature of Quantities 2 (OCR) Nature of Quantities 2 MS (OCR) A-Level Qs: overlapping content

#### Vector Subtraction

Vector subtraction seems a little more abstract on the surface of it - what does it  actually mean to subtract one vector from another? Typically we might use vector subtraction when we are looking to find the 'change in' a certain vector.

Imagine I'm cycling along at 10 m/s travelling North and turn to travel at 10 m/s West. Clearly, my overall speed has not changed, though my direction has.  As velocity is a vector quantity this means that my velocity has changed. Therefore To find the change in velocity, I would typically subtract my initial velocity from my final velocity.

## Video Lessons

 Khan Academy Adding and Subtracting Vectors Subtracting vectors example Physics Online Subtracting Vectors Study Nova Subtraction of Vectors Multiplication not required

## Resources

 IB Physics Topic 1 Notes IB-Physics.net Chapter 1 Summary IB Revision Notes Isaac Physics Vector Subtraction Mr. G 1.3 Teaching Notes 1.3 Student Notes

## Questions

 Grade Gorilla 1.3 (Vectors & Scalars) MCQs Topic 1 (Measurements) Final Quiz Quick IB Specific Mixed MCQs Mr. G 1.3 Formative Assessment Topic 1 Summary Qs IB Specific Questions