Understanding Scalar And Vector Quantities - IGCSE & GCSE Physics

Transcript

This video is about understanding scalar and vector quantities. All physical quantities can be classified as scalars or vectors. Scalars have a magnitude or size only.

For example, the athlete runs a distance of 100 meters. Vectors have a magnitude and a direction. Here the athlete runs a distance of 100 meters with a direction due east.

A vector describes a situation in more detail. The direction part of the vector can be shown in many ways. In this example, the vector is

shown with a plus or minus sign. The diagram shows a box being pulled by two forces, 15 Newtons in the negative direction, and three Newtons in the positive direction. The magnitude of the

resultant force is 12 Newtons. This comes from ignoring the axis given to get 15 minus three is equal to 12, or three minus 15 is equal to minus 12 Newtons, where the magnitude is still 12 Newtons. When described as a vector,

this is minus 12 Newtons. This means that the force acts in the negative direction, according to the axes given. Always look at the situation in the diagram really carefully.

The direction part of the vector can also be given by an angle. In this second example, the force has a magnitude of 50 Newtons. This is the scalar, but as a vector,

it can be described as 50 Newtons at an angle of 15 degrees to the horizontal. To get full marks in this question, you must say that the angle is 15 degrees to the horizontal, or the description is not complete. A quantity is also a vector

when the direction part is explained with instructions. In this example, the balloon is traveling at a speed of 200 meters per second, but as a vector we can say that the velocity is 200 meters per second upwards. Think about the words used in

a question and what this means. Most often the language used to describe a quantity can tell us whether it is a scalar or a vector. Examples include; displacement, the distance in a certain direction, and velocity the speed in a certain direction.

How do you know that momentum is a vector? Well, the equation for momentum is momentum is equal to mass times velocity. Mass is a scalar, and velocity is a vector. So, momentum must also be a vector.

Don't be fooled by quantities such as electric charge either. Whilst charge can be positive and negative, this is related to the magnitude of the quantity and not the direction of a moving charge.

Memorise these most common vector quantities ready for your exam. Vectors must be drawn clearly and adhere to certain rules. The length of the arrow must represent

the magnitude of the vector, and the arrow must show the direction of the vector. For example, we want to draw a vector of length four in the positive direction. This is shown correctly here. This arrow, however, is the correct

length, but facing in the wrong direction to represent the vector correctly. Always draw your vector arrows coming out of the object, not going into it. Now we have a vector of magnitude three in the negative direction with an incorrect example below.

This is also in the negative direction, but with a magnitude of one and not three. Always draw vectors with a ruler. Here is an example question testing your knowledge of scalar and vector terminology.

Before starting this question, it is important to identify; the key information, the command words used and the number of marks available. A journalist reporting on a running race states that the winner ran a distance of 52 kilometers, but with an overall

displacement of five kilometers due north. Explain what this means, for two marks. So we need to make two statements for our answer. A distance of 42 kilometers means

that the race was 42 kilometers long. This is the first mark, and the overall displacement of the race was five kilometers due north, which means the race finished five kilometers away from where it started, and this was exactly north of the starting point.

This is for the second mark. Remember the number of marks is the number of points you need to make in your written answer. In summary, scalars have a magnitude only, but vectors have a magnitude and a direction.

Vector direction can be represented in several ways with a plus or minus sign, an angle, instructions or with language. For example, displacement is the vector quantity of distance. When drawing a vector, the length of

the arrow represents the magnitude. The direction of the arrow represents the direction of the vector. Don't forget to check out all our other fantastic revision resources.

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