CIE AS Physics (9702) 2019-2021

Revision Notes

1.1.4 Scalars & Vectors

What are Scalar & Vector Quantities?

  • A scalar is a quantity which only has a magnitude (size)
  • A vector is a quantity which has both a magnitude and a direction
  • For example, if a person goes on a hike in the woods to a location which is a couple of miles from their starting point
    • As the crow flies, their displacement will only be a few miles but the distance they 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 an object has travelled overall, but not the direction it has travelled in
  • Displacement is a vector quantity because it describes how far an object is from where it started and in what direction
  • There are a number of common scalar and vector quantities

          Scalars and Vectors Table

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

Exam Tip

Do you have trouble figuring out if a quantity is a vector or a scalar? Just think – can this quantity have a minus sign? For example – can you have negative energy? No. Can you have negative displacement? Yes!

Combining Vectors

  • Vectors are represented by an arrow
    • The arrowhead indicates the direction of the vector
    • The length of the arrow represents the magnitude
  • Vectors can be combined by adding or subtracting them from each other
  • There are two methods that can be used to combine vectors: the triangle method and the parallelogram method
  • To combine vectors using the 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
  • To combine vectors using the 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
  • When two or more vectors are added together (or one is subtracted from the other), a single vector is formed and is known as the resultant vector

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

  • Coplanar forces can be represented by vector triangles
  • In equilibrium, these are closed vector triangles. The vectors, when joined together, form a closed path

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

  • Two vectors can be represented by a single resultant vector that has the same effect
  • A single resultant vector can be resolved and represented by two vectors, which in combination have the same effect as the original one
  • When a single resultant vector is broken down into its parts, those parts are called components
  • For example, 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 using trigonometry

Resolving Vectors, downloadable AS & A Level Physics revision notes

 

  • For the horizontal component, Fx = Fcosθ
  • For the vertical component, Fy = Fsinθ

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