17. Scalar & Vector Quantities - What They Are | Examples

1. Scalar Quantities (Scalars)

• Definition: Physical quantities that only have magnitude (size) but no direction.

• Magnitude: This is just a numerical value or size. For example, if a car travels at 22 m/s, "22" is the magnitude.

• Common Examples:

  • Speed (e.g., 20 m/s)

  • Distance (e.g., 5 meters)

  • Mass (e.g., 10 kg)

  • Temperature (e.g., 25°C)

  • Time (e.g., 60 seconds)

2. Vector Quantities (Vectors)

• Definition: Physical quantities that have both magnitude and direction.

• Distinction: A vector gives you more information than a scalar because it tells you where or which way something is going.

• Common Examples:

  • Velocity (Speed in a given direction, e.g., 20 m/s North)

  • Displacement (Distance in a given direction, e.g., 3 km East)

  • Acceleration

  • Force (e.g., 10 N downwards)

  • Momentum

3. Distance vs. Displacement (The Walk Example)

• Distance (Scalar): If you walk 3 km from point A, you could end up anywhere on a circle with a 3 km radius. We don't know your final position because we don't have a direction.

• Displacement (Vector): If you walk 3 km East, we know exactly where you are. The magnitude is 3 km and the direction is East.

4. Representing Vectors

Using Arrows

• Length: The length of the arrow represents the magnitude of the vector. A longer arrow means a larger magnitude.

• Direction: The way the arrow points indicates the direction of the quantity.

Negative Vectors

• A vector can be described as negative if it acts in the opposite direction to the reference direction.

• Example: "2 km West" can be written as "-2 km East" because it is effectively backwards in the East direction.

5. Summary Comparison