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IGCSE CIE Physics - Scalars and Vectors

CHAPTER 1 Physical quantities and units

· Physics,IGCSE CIE,Vectors,Scalars

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*.

- We can add vectors directly

*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**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: Is a rotating vector with constant magnitude on a plane a constant vector?

A: No, because its direction is varying! 💃🏻.

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! 🤘

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

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