Revision: Vectors and Scalars
Introduction
Physical quantities (anything that can be measured/calculated in physics) can be classified under two main headings. Vectors and Scalars.
Definitions of Vectors and Scalars
A vector quantity is any quantity that has both magnitude (size) and direction. Examples of vectors are velocity, acceleration, force, momentum.
A scalar quantity is any quantity that has magnitude only. Direction is not taken into account with scalar quantities. Examples of scalars are speed, pressure, temperature, energy.
Vectors are represented by arrows. The length of the arrow giving an indication of the magnitude of the vector, the direction of the arrow indicating the vector's direction.
Addition of Vectors: Finding the Resultant
When we add two or more vectors, it is absolutely crucial to take the direction of the vectors into account. The process of adding two or more vectors is known as finding the RESULTANT of the vectors. The resultant of two or more vectors is the single vector that could replace those vectors and still have the same effect in terms of both magnitude and direction.
When two or more vectors are acting in the same direction in the same straight line, the resultant vector is a vector in the same direction, with a magnitude equal to the sum of the magnitudes of the other vectors.
Things are slightly more complicated when vectors are not in a straight line. For example, when vectors are perpendicular to each other.
Perpendicular Vectors and Vector Triangles
When we are finding the resultant of two vectors acting perpendicular to each other, we can use Pythagoras' theorem and basic trigonometry to find the resultant vectors magnitude and direction.
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