Vectors and Scalars in Linear Motion

SCALARS

• Definition: Quantities that have magnitude but no direction.
• Examples:
  • Distance: Only numerical value and unit needed (e.g., 400 m).
  • Other Scalars:
  • Time
  • Energy
  • Volume
  • Speed
  • Temperature
  • Mass
  • Density
  • Electric Charge
  • Voltage

VECTORS

• Definition: Quantities that possess both magnitude and direction.
• Examples:
  • Force: e.g., 6 N upwards.
  • Other Vectors:
  • Displacement
  • Velocity
  • Acceleration
  • Momentum
  • Weight

VECTORS AS ARROWS

• Representation: Vectors can be visually depicted as arrows.
  • Length of the Arrow: Indicates the magnitude.
  • Arrowhead: Represents the direction.
• Scale: In some vector diagrams, the length of the arrow is to scale, accurately depicting the vector's magnitude.
• Example: A force of 4 N to the left acting on a toy car is shown as an arrow pointing left.

POINT OF APPLICATION

• Vector Diagram Variation: Vector diagrams can differ based on the scenario depicted.
  • For example:
  • Force on a Ball:
    • Kicking force: 95 N East (acting at the point of contact between the ball and the foot).
    • Friction force: 20 N West (acting between the ball and the ground).
    • Kicking force magnitude larger than frictional force.

ADDING VECTORS GRAPHICALLY

• Method: Graphically add vectors using vector diagrams by arranging them "head to tail."
• Resultant Vector: Drawn from the tail of the first vector to the head of the last.
• Example:
  • Adding a displacement of 15 m East and 5 m East results in:
  • Resultant vector = 20 m East, shown in red in the diagram.

SUBTRACTING VECTORS GRAPHICALLY

• Method: Similar to addition but involves negating the vector you wish to subtract (change the arrowhead direction).
• Example:
  • To determine the difference when subtracting a vector results in:
  • Given: extbf{2} - extbf{1} (negate the direction of extbf{1}).
  • Resultant vector shown in red: ext{Δ} = 6 ext{ m/s West}.