PHY C1: Scalars and Vectors

What are Scalars?

Physical quantities that have a magnitude only.

What are Vectors?

Physical quantities that have both a magnitude and a direction.

What are some examples of Scalar Quantities?

Distance, speed, energy, mass, time, temperature.

What are some examples of Vector Quantities?

Displacement, velocity, moment, weight, acceleration, momentum.

How is a Vector represented?

By an arrow: length represents magnitude, direction represents direction.

What is Vector Addition - Polygon Law? (For any number of vectors)

Two or more vectors may be added by joining the head of one vector to the tail of another. The resultant vector joins the tail of the first to the head of the last vector.

What is Vector Addition - Parallelogram Law? (For only two vectors)

If vectors form the sides of a parallelogram starting/ending at same point, the resultant vector is the diagonal of the parallelogram.

Is Vector Addition commutative?

Yes (A + B = B + A).

What is Vector Subtraction?

Can be rewritten as adding a negative vector (A - B = A + (-B)). The negative vector points opposite to its original direction.

How can any vector be resolved?

Into two perpendicular components (e.g., vertical/horizontal, or parallel/perpendicular to a slope).

What is the magnitude of a vector component relative to the original vector?

Smaller, unless the vector lies along an axis.

How can vector components be "recombined"?

To give the magnitude and direction of the original vector.