CIE AS Physics (9702) exams from 2022

Revision Notes

1.1.3 Scalars & Vectors

What are Scalar & Vector Quantities?

  • A scalar is a quantity which only has a magnitude
  • A vector is a quantity which has both a magnitude and a direction
  • For example, say you go on a hike in the woods to a location which is a couple of miles from your start point
    • As the crow flies, your displacement will only be a few miles but the distance you walked will be much longer

Displacement v distance, downloadable AS & A Level Physics revision notes

Displacement is a vector while distance is a scalar quantity

  • Distance is a scalar quantity because it describes how far you have travelled overall, but not the direction
  • Displacement is a vector quantity because it tells you how far you are from where you started and in what direction
  • The table shows a variety of scalar and vector quantities you will come across in Physics:

         Scalars and vectors table

Scalars and Vectors Table, downloadable AS & A Level Physics revision notes

Combining Vectors

  • Vectors are represented by an arrow to indicate its direction and length to represent its magnitude
  • We can combine vectors by adding or subtracting them from each other
  • There are two methods you can use to combine vectors: the triangle method and the parallelogram method

Triangle method

  • Step 1: link the vectors head-to-tail
  • Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

Parallelogram method

  • Step 1: link the vectors tail-to-tail
  • Step 2: complete the resulting parallelogram
  • Step 3: the resultant vector is the diagonal of the parallelogram

Vector addition
Vector Addition, downloadable AS & A Level Physics revision notes

 

Vector subtraction

Vector Subtraction, downloadable AS & A Level Physics revision notes

 

Condition for equilibrium

Vector Equilibrium, downloadable AS & A Level Physics revision notes

If three forces acting on an object are in equilibrium, they form a closed triangle

 

Resolving Vectors

  • A force vector of magnitude F and an angle of θ to the horizontal is shown below

Representing Vectors, downloadable AS & A Level Physics revision notes

  • It is possible to resolve this vector into its horizontal and vertical components

Resolving Vectors, downloadable AS & A Level Physics revision notes

 

  • Fx = Fcosθ
  • Fy = Fsinθ
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