Vectors – AS Physics Revision


The addition of two vectors a and b

The addition of two vectors a and b (Photo credit: Wikipedia)

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

About Matt

I like writing, filmmaking, programming and gaming, and prefer creating media to consuming it. On the topic of consumption, I'm also a big fan of eating.
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