Scalar and Vector Physics

Physics describes how things move, interact, and change; it relies on measurements called quantities.
Quantities come in different kinds; not all quantities behave the same way. Distinguishing quantity types is foundational to physics.
Everyday relevance: physics appears in ordinary tasks and decisions, often without conscious awareness.

Setup: two volunteers, both blindfolded; one guided by the class with simple steps; the other guided by combined steps and directions.
Procedure:
- Step 1: Two volunteers are chosen and blindfolded.
- Step 2: The first volunteer is guided by the class with a set of steps to reach the prize.
- Step 3: The second volunteer is guided by the class with different instructions (including directions).
- Step 4: Both enter the room, are blindfolded again, and then re-enter.
Questions to reflect:
1) What is similar between the experiences of the first and second volunteers?
2) How do their experiences differ?
Concept connection: comparing experiences traces how different instruction sets describe motion; in physics, some descriptions specify only how far to go (scalar-like steps), while others specify both how far and which way to go (vector-like directions).

Essential question: Why is knowing how fast something is moving not enough without knowing its direction?
Scalar quantities:
- Have only magnitude (a numerical value with a unit).
- Examples: temperature, time, speed, distance, mass.
- Notations: a scalar is fully described by its magnitude and unit, e.g.,
- Temperature: $T = 38^{ frac{\circ}{}}C$ or simply 38°C.
- Speed: $v = 60\ \mathrm{km/h}$ (scalar, magnitude only).
- Time: $t = 24\ \mathrm{h}$ .
- Distance: $d = 1\ \mathrm{m}$ .
- Mass: $m = 55\ \mathrm{kg}$ .
Vector quantities:
- Have both magnitude and direction.
- Represented by arrows in a diagram; may be described by coordinates or components.
- Examples: displacement, force, velocity (when specified with a direction), etc.
- Example given: $ext{Displacement example: } 33\ \mathrm{m}\ \text{North};\ 3\ \mathrm{m}\ \text{East}.$
Quick distinction recap:
- Scalar: magnitude only.
- Vector: magnitude and direction.
- In the unit context, some quantities (like force) are vectors, while many temporal and distance-type quantities are scalars.

Task: classify each quantity as scalar or vector.
- Temperature: Scalar (T = 38°C).
- Speed: Scalar (v = 60 km/h).
- Time: Scalar (t = 24 h).
- Distance: Scalar (d = 1 m).
- Mass: Scalar (m = 55 kg).
- Force: Vector (F = -50 N, direction matters).
Note on notation: direction is often given by a positive/negative sign or a directional label (e.g., North, East, Up, Right, Forward as positive; South, West, Down, Left, Backward as negative).

Direction often encoded with signs or labels:
- Positive directions: North, East, Up, Right, Forward.
- Negative directions: South, West, Down, Left, Backward.
Example mapping used in the course:
- Positive: North, East, Up, Right, Forward.
- Negative: South, West, Down, Left, Backward.

Speed: how fast something is moving; no specified direction (scalar).
- Example: v = 60 km/h (speed only).
Velocity: how fast something moves and in which direction (vector).
- Clarifies both magnitude and heading.
Notation guidance: when the direction is included, velocity is a vector; otherwise, speed is a scalar.

Distance (scalar):
- The total path length traveled; direction is not specified.
- Example: traveling along a path that measures 5 m, then 3 m, total distance = 8 m.
Displacement (vector):
- The shortest straight-line distance from the starting point to the ending point.
- Includes direction; can be written as a vector, e.g., magnitude with a direction.
- Example given: if the start is (0,0) and end is (300 m, 0), displacement D = 300 m east (direction specified).

Process to visualize a vector on a coordinate plane:
1) Draw coordinate axes (x-axis and y-axis).
2) Let the x-axis represent East-West and the y-axis represent North-South.
3) Choose a scale (e.g., 1 cm = 10 Newtons or 1 cm = 100 km/h).
4) Label the vector with its symbol (e.g., F for Force).
5) Indicate the vector’s direction and angle from an axis.
Example: F = 50 N east (vector on the axes).
Exercise: such steps help visually connect how far a quantity moves and in what direction.