Scalar Vector speed, distance, time, temperature, mass, energy a quantity described by magnitude only examples include: speed, distance, time, temperature, mass, energy Vector a quantity described by magnitude and direction examples include: velocity, displacement, force, momentum, electric and magnetic fields

Scalar or Vector? 5 mph 5 mph north 15 m/s northwest 1.2 N west 10 m/s

Vectors What if the vectors are NOT parallel: Vectors have magnitude and direction. They add or subtract depending on their directions. Parallel vectors are pretty simple: 50 N 100 N = + 50 N 50 N = 0 N + 50 N What if the vectors are NOT parallel: Example: What if I walked 16 km East and 12 km North The result is a NET movement of 20 km Northeast 20 km Northeast 12 km North Resultant Vector 16 km East Component Vectors

Examples include: A = 20 m/s at 35° B = 120 N at 300° Vectors are usually named with capital letters with arrows above the letter. They are represented graphically as arrows. The length of the arrow corresponds to the magnitude of the vector. The direction the arrow points is the vector direction. Examples include: A = 20 m/s at 35° B = 120 N at 300° C = 5.8 m/s west or 180°

Vector Addition Triangle (Head-to-Tail) Method vectors may be added graphically or analytically Triangle (Head-to-Tail) Method 1. Draw the first vector with the proper length and direction. 2. Draw the second vector with the proper length and direction originating from the head of the first vector. 3. The resultant vector is the vector originating at the tail of the first vector and terminating at the head of the second vector. 4. Measure the length and orientation angle of the resultant.

Adding vectors Head-to-tail A A B C B A + B = C

Parallelogram (Tail-to-Tail) Method 1. Draw both vectors with proper length and direction originating from the same point. 2. Complete a parallelogram using the two vectors as two of the sides. 3. Draw the resultant vector as the diagonal originating from the tails. 4. Measure the length and angle of the resultant vector.

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