Vectors
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PGCE Comments - TO DO LIST - Introduction - Examples - Mathematical Properties - Addition - Components - Importance - Important Quantities, Equations, and Concepts

`TO DO' LIST

Please mention that although a rotation about an axis can be represented as a vector which statisfies your definition, the addition (composition) of two successive rotations about distinct axes is not obtained by simply adding the corresponding vectors. A better definition is: something which has direction and magnitude and adds by the parallelogram rule. (Alex)
Mention that the direction of a vector is measured from its tail.
Also include explanations of the ways in which to specify direction (e.g. bearing, compass points, angle from vertical, etc.)
Include exam-type questions involving flowing rivers or aeroplanes in wind. These questions link displacement, velocity and time and also test the learners understanding of vectors combining to give a combined result (i.e. resultant).
Mention that displacement at a point is the directed line from the start to that point.
Rewrite section on velocity to make clear the distinction between average and instantaneous rates of change (velocity and speed). The $\Delta$ 's in the equations imply we are calculating average quantities. Mention that we take the limit of a small time interval to give instantaneous quantities. Perhaps the example of a parabola with average gradient and gradient of tangent can be used as an illustration. Else defer until chapter on Graphs and Equations of Motion. Instantaneous velocity: reading on the speedometer in a direction tangent to the path. Instantaneous speed is magnitude of instantaneous velocity but average speed is not equal to magnitude of average velocity. Average speed and average velocity are the total distance and resultant displacement over the time interval related to that part of the path. The example of the circular track uses these definitions and is an important illustration of the differences. Instantaneous calculated at a certain instant in time while average is calculated over an interval.
Include relative velocity.
Address PGCE comments above and comments in the text.