Scalars and Vectors Physical Quantities: Anything that can be measured. Ex. Speed, distance, time, weight, etc. Scalar Quantity: Needs only a number and proper units to completely describe. Ex. Time, temperature, length Vector Quantity: Requires both a number (called its “magnitude”) and a direction, along with proper units, to fully describe. Ex.Velocity, displacement, acceleration, force

Scalars and Vectors (2) Vectors in detail: Represented by arrows drawn at a given angle from a reference axis. A vector consists of two parts: A magnitude, which is “how much”, and a direction (usually an angle). Y X 

Scalars and Vectors (3) Adding Vectors: Called finding the sum, resultant, or net vector. Vectors can not usually be simply added like regular numbers. Three Cases: Collinear Perpendicular Arbitrary

Scalars and Vectors (4) 1) Collinear: In the same direction or 180° opposite. To add collinear vectors: Verify that vectors are collinear – is there 0  or 180  between them? If they are in the same direction, add their magnitudes. If in opposite directions, subtract their magnitudes. Largest vector determines direction. Examples: Add the following vectors: 1. V 1 = 5.0 at 0°, V 2 = 7.0 at 0° 2. V 1 = 3.0 at 0°. V 2 = 8.0 at 180°

Scalars and Vectors (5) 2) Perpendicular vectors: Draw the vectors “Tip to Tail” and roughly to scale. This will form a right triangle. The Hypotenuse of the right triangle will be the resultant vector. Use the Pythagorean theorem to find this. Use Trig. functions (usually inverse tangent) to find the angle of the resultant. Example: Add the following vectors to find the resultant: V 1 = 5.0 at 0°, V 2 = 3.0 at 90°