What a Vector is:

- A vector is a variable that has a direction as well as a magnitude
- (As opposed to a scalar, which only has the magnitude)
- The direction has to be relative to something, for it to have any meaning
- For instance, it could be relative to North
- I will attempt to explain this without diagrams…

Some Example Vectors:

- Velocity is a vector (it’s speed, but in a direction)
- Its magnitude is measured in ms-1, and its direction is measured in degrees (or radians, I guess – any way of measuring an angle)
- Average velocity is the final displacement divided by total time, but it might not have been a constant velocity the whole time – instantaneous velocity might have varied
- Objects in circular motion have a constant speed, but their velocity is always changing, because the direction to centre of the circle changes as the object goes round
- Displacement (distance in a direction) is also a vector, measured in metres, with an angle
- Velocity = Displacement /Time in the same way that Speed = Distance / Time
- Force is a vector

Representing Vectors:

- To indicate that something is a vector, write it in bold, or underline it
- You can represent vectors as arrows:
- The length of the arrow indicates the magnitude of the vector
- The direction of the arrow indicates… the direction of the vector
- You can add two or more vectors graphically, by placing one vector arrow on the end of the other vector arrow
- The resultant vector is an arrow from the start of the first arrow to the end of the last arrow

Calculations on Vectors:

- Any 2D vector can be split into a horizontal component and a vertical component
- You can
~~pythagorize~~use Pythagoras’ theorem, because there’s a right angle between the horizontal component and the vertical component, making the vector you’re splitting up the hypotenuse - Phythagoras’ theorem goes like this: a^2 = b^2 + c^2, where:
- a is the length of the hypotenuse (the resultant vector you’re splitting up)
- b and c are the lengths of the horizontal and vertical components
- Trigonometry SOH CAH TOA is also handy

Free Body Force Diagrams

- A free body diagram shows the forces acting on an object as arrows
- You can add up these arrows using the methods above, to get a resultant force
- The arrows on the diagram start from the middle of the object and point in the direction the (vector) force is acting in
- If the resultant force is zero, the object is at equilibrium
- Moving at a constant speed also counts as equilibrium, so not moving at all is called static equilibrium

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