IGCSE CIE Physics - Scalars and Vectors

• distinguish between scalar and vector quantities and give examples of each

• add and subtract coplanar vectors

• represent a vector as two perpendicular components

There are roughly two kinds of Physical quantities: scalars and vectors

• A scalar quantity has magnitude only.
• A vector quantity has magnitude and direction. 
  • The "arrowhead" points at the direction of the vector.

Examples for scalar: distance, speed, mass, charge, energy

Examples for vector: displacement, velocity, force, acceleration, momentum, energy flow

You may wonder what good does a vector do! A fair question. For the poor man above, he will definitely want to know the direction of the arrow before shooting! Magnitude alone is not enough to describe the arrow's motion. In Physics, when necessity calls, we invent! Kind of feel like an entrepreneur, huh?

• When scalars are added, they are simply arithmetically added. 
• When physical vectors act on a same point, we can add the vectors - beware! their directions must be taken into consideration!
  • We can add vectors directly only if  they lay on the same line. If two vectors are in opposite directions, one of them will have a minus sign. 
  • If vectors act at other angle, we must use triangle of vectors. 

triangle of vectors : a + b :

• you can move a or b  parallelly. 
• draw the resultant ( the vector = a + b ) vector from one vector's tail to another vector's head.
• a , b and the resultant vector together have to form a closed triangle. 

On the other hand:

• Any vector v can be resolved into two components at right angles to each other. The two resolved vectors, namely v_x and v_y , are respectively:
  • v_x is |v| cos θ, where  |v|  is the magnitude of the vector v , and θ is the angle between v and v_x.
  • v_y is |v| sin θ  

Caution! 🧐In IGCSE CIE Physics, they may ask you to calculate the resolved vectors!

Q: If I make up some crazy stuffs like: [ 2 apples, 5 oranges ] ...... is this a vector?

A: No, actually a vector also has to rotate like a vector... you can't rotate that thing (at least not meaningfully).

That's all, see you next time! 🤘

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Written by Shing, Physics & Mathematics Specialist @ TUTTEE

Reference:

Richard Woodside, Chris Mee - Cambridge International AS_A Level Physics Revision Education, 2nd Edition

David Sang, Graham Jones, Gurinder Chadha, Richard Woodside - Cambridge International AS and A Level Physics Coursebook, 2nd Edition