Scalars and Vectors

Scalars and Vectors

Up until this unit, there are certain concepts in Physics that are used either interchangeably or downright incorrectly in "everyday" language.

Scalars and Vectors is a new concept that will be used continuously throughout Physics all the way up to Advanced Higher and beyond. The difference between a Scalar and Vector is as follows:-

Scalar - Has a magnitude only (eg 45 m, 45 ms-1, 45 kg)

Vector - Has a magnitude and direction (eg 45 m North, 45ms-1 East)


Speed and Velocity

Up to now these two words have been seen as interchangeable. This is no longer the case. The following must now be used when describing motion:-

Speed - Scalar quantity (magnitude only).

Velocity - Vector quantity (magnitude and direction).


Distance and Displacement

Up to now, only distance has been discussed. Now, its Vector equivalent will also be used:-

Distance - Scalar quantity - How far the object actually moved.

Displacement - Vector quantity - How far is the end point from the start.


When to use which?

During calculations, you must remain consistent with either use of Scalar or Vectors. For example, using distance will give an object's speed, whereas using Displacement will give an object's Velocity.


Vectors and Direction

As stated above, in order to give a full description to a Vector, a direction must be given. There are several methods for giving a direction that can be used in Physics, with the two main methods described below.

1.Angle from a reference point.

2.Three figure Bearing.

What is the displacement of a runner who travels the route A-B-C?

Using Pythagoras to find the magnitude:-

displacement = square root of (42 + 32)

= 5 km

Using Trigonometry to find the direction :-

Tan-1 (θ) = (4 / 3)

θ = 53°

Note - This value of 53° is not enough information to give a direction clearly. You must give a position and direction of this angle to give the information clearly.

Method 1 - Displacement 5 km at an angle of 53° East of North.


The above method is useful as it requires no further work to give an answer. This method, however, risks getting confused with direction (eg is it East of North or North of East ?).

In order to avoid this confusion, three figure Bearings can be used. A three figure Bearing is the angle clockwise from North. This prevents the problems of direction in any answers. The diagram below shows the compass points given as three figure Bearings:-

Method 2 - Displacement 5 km at a Bearing of 053 .


Note - Either method is acceptable, unless the question specifically asks for a particular method.

Air Traffic Controller

You would calmly and carefully guide aircraft pilots during their take off, their flight and landing

You'd help them avoid other aircraft and deal with difficult weather conditions so the crew and passengers arrive safely and on time.

You'd be responsible for giving clear instructions to make sure that aircraft travelling through UK airspace are kept a safe distance apart.

You'd also respond to emergency distress calls, working under pressure to help the aircraft land safely. For example, this might include instructing and guiding a light aeroplane that has lost its way in bad weather.

This is a responsible job where you'd need to concentrate. You'd receive and need to interpret and check a lot of information quickly.

Air Traffic Controller

Working as an Air Traffic Controller

A Career as an Air Traffic Controller

Salary: from £40,000 to £105,000 per year

Controller working hours: 40 hours a week on a shift basis, including days, nights, weekends and public holidays. During a shift, you might guide aircraft for up to two hours, followed by a half-hour break.

Typical entry requirements: Training course with the National Air Traffic Services (NATS) or with the armed services. To get into this training you will need qualifications at SCQF Level 5 or above.

Skills required:

  • Taking responsibility

  • Developing a plan

  • Sorting

  • Understanding

  • Analysing

  • Working with technology

  • Verbal communication

  • Observation

  • Working with numbers

  • Problem solving