Vectors and scalars


Vectors and scalars

POSTED IN O/A Level PHYSICS, MECHANICS



Scalar quantities are things like mass and speed, they only have a size. Vector quantities are things like velocity and acceleration, they not only have a size but also a direction such as 20ms-1 forward.

Notation

Vectors can be notated in several different ways:
  • Dynamic image 0 - a vector from point a to b
  • a - a vector called a, usually used in typed algebra
  • a - a vector called a, usually used in handwritten algebra

Adding vectors

Vectors can be represented b arrows with the length of the arrow representing the size of the vector (if drawn to scale). Vectors can be added by drawing them tip to tail and then finding the resultant of the vectors - the vector from the tail of the first vector to the tip of the last vector. A simple example:
Vector addition
Here the resultant R is a single vector which could replace all the other vectors. If the drawing is to scale the size of the resultant can be measured using a ruler, but remember that the vectors may be representing a quantity such as velocity and so the units won't be cm but rather ms-1

Resolving vectors

Resolving a vector involves splitting into two other vectors which add together to give the total vector. This is used to separate horizontal motion from vertical motion by separating the vector into two perpendicular components:
resolution of vectors
Here the vector A has been resolved into two vectors, Ax and Ay such that Ax + Ay = A
Some simple trigonometry allows the size of the two vectors to be calculated:
  • Ax = A cosDynamic image 1
  • Ay = A sinDynamic image 1

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