Physics: Scalar and Vector Quantities

Scalar Quantities

• Scalar quantities only have magnitude.
• Examples of scalar quantities include:
  • Mass
  • Distance
  • Area
  • Volume
  • Time
  • Speed
  • Density
  • Pressure
  • Energy (including gravitational potential and kinetic energy)
  • Work done
  • Power
  • Temperature
  • Current
  • Potential difference
  • Resistance
• All base quantities are scalars.

Vector Quantities

• Vector quantities have both magnitude and direction.
• Examples of vector quantities include:
  • Displacement (the vector equivalent of distance)
  • Velocity (the vector equivalent of speed)
  • Acceleration (the derivative of velocity)
  • Force (including weight and drag force)
  • Momentum
  • Magnetic field
• Direction conventions are used to label and describe the direction of vector quantities.
  • Typically, right is positive and left is negative.
• The length of a vector arrow is proportional to its magnitude.

Direction Conventions

• Direction conventions help understand the direction of vector quantities.
• They establish which direction is positive and which is negative.
• This simplifies calculations by using positive and negative values to represent the magnitude and direction.

Resultant Force

• When multiple forces act on an object, their combined effect is called the resultant force.
• The resultant force is calculated by adding the individual forces, taking into account their direction.
• The direction of the resultant force is determined by the direction convention.

Example: Bus traveling at 30 km/h towards the left

• Speed: 30 km/h (scalar, magnitude only)
• Velocity: -30 km/h (vector, magnitude and direction towards the left, which is negative according to the convention)
• Direction Convention: In this scenario, left is negative and right is positive.
• Resultant Force: If a box has two forces acting on it, one with +5 N and the other with -2 N, the resultant force is +3 N, indicating a force of 3 N towards the right.