Scalar and Vector quantities

• Scalar and vector quantities are treated differently in calculations
• Scalar quantities:

  • Can be measured and only have a magnitude or size
  • Examples include temperature, mass, energy, distance, speed, and density
• Calculations involving scalar quantities:

  • Adding scalars: find the sum by adding their values together
  • Subtracting scalars: subtract one value from another
• Vector quantities have both magnitude and an associated direction
• Scalar and vector quantities are treated differently in calculations
• Examples of vector quantities include:

  • Force, e.g. 20 newtons (N) to the left
  • Displacement, e.g. 50 kilometres (km) east
  • Velocity, e.g. 11 metres per second (m/s) upwards
  • Acceleration, e.g. 9.8 metres per second squared (m/s²) downwards
  • Momentum, e.g. 250 kilogram metres per second (kg m/s) south west
• Resultant force:

  • The single force that could replace all the forces acting on an object, found by adding these together
  • If all the forces are balanced, the resultant force is zero
  • A single force that has the same effect as two or more forces acting together
• The direction of a vector can be given in a written description or drawn as an arrow
• The length of an arrow represents the magnitude of the quantity
• Two forces in the same direction produce a resultant force that is greater than either individual force

  • Simply add the magnitudes of the two forces together
• Example:

  • Two forces, 3 newtons (N) and 2 N, act to the right
  • Calculate the resultant force: 3 N + 2 N = 5 N to the right
• Two forces in opposite directions produce a resultant force that is smaller than either individual force

  • It is often easiest to subtract the magnitude of the smaller force from the magnitude of the larger force
• Example:

  • A force of 5 N acts to the right, and a force of 3 N act to the left
  • Calculate the resultant force: 5 N - 3 N = 2 N to the right
• Free body diagrams are used to describe situations where several forces act on an object
• Vector diagrams are used to resolve (break down) a single force into two forces acting at right angles to each other