Physics: Vectors and Scalars

Vectors and Scalars

• A vector has both magnitude and direction.
• A scalar has only magnitude.
• Scalars are generally non-negative, but vectors can be negative as they have a direction associated with them.

Examples of Vectors and Scalars

• Speed is a scalar quantity.
• Velocity is a vector quantity.
• Distance is a scalar quantity.
• Displacement is a vector quantity.
• Time is a scalar quantity.
• Momentum is a vector quantity.
• Acceleration is a vector quantity.
• Energy is a scalar quantity.
• Force is a vector quantity.
• Mass is a scalar quantity.

Displacement and Velocity

• Displacement can be negative if the direction is considered (e.g., a ball thrown off a cliff).
• The zero point of a vector can be chosen arbitrarily, depending on the context (e.g., setting the zero point at the bottom of a cliff).
• Velocity is speed with direction (e.g., 10 m/s vs. 10 m/s at 30° above the horizontal).
• Even if the speed is constant, the velocity can change if the direction changes (e.g., a car traveling around a roundabout).

Representing Vectors

• Vectors can be represented by arrows, with their size/length representing the vector magnitude.

Object Interaction

Forces

• A force is a push or pull that acts on an object due to interaction with another object.
• Forces can be classified into two types:
  • Non-Contact Forces:
    • Electrostatic forces (caused by charges)
    • Gravitational forces (caused by mass)
  • Contact Forces:
    • Normal contact force (opposite direction to contact)
    • Friction (caused by surface roughness when moving in contact)