Understanding Magnitudes and Vectors in Physics

Understanding Magnitudes in Physics

In physics, a physical quantity is operationally defined by a number and its respective unit of measurement. The magnitude is the size or module of this quantity.

Types of Magnitudes

Scalar Magnitudes

Scalar magnitudes, such as length, volume, time, and temperature, are fully expressed by their module (size).

Vector Magnitudes

Vector magnitudes, such as velocity, force, momentum, and acceleration, are associated with a direction. They are related to directed segments (rays) referred to as vectors. Key components of a vector include:

• Module (Magnitude and Size): The length of the vector.
• Point of Application: The origin of the vector.
• Direction: The angle between the vector and the positive horizontal direction.
• Sense: Indicated by the arrowhead.

Vector Summation

Vector summation involves geometrically combining vectors. There are two primary methods: graphical and analytical.

Graphical Methods

Parallelogram Method

This method is used to add two vectors. The vectors are drawn with the same origin, and a parallelogram is constructed. The diagonal from the origin to the opposite corner represents the resultant vector. For vector subtraction, add the first vector with the opposite of the second. Place them at a common origin, and the difference vector extends from the end of the subtrahend vector to the end of the minuend vector.

Polygon Method

This method is used to add three or more vectors. The vectors are placed head-to-tail. Starting from a common origin, each subsequent vector is drawn parallel and equal in length to the original vectors, rotating clockwise. The resultant vector extends from the origin of the system to the end of the last parallel vector drawn. A vector parallel to another with the same length and direction is called equipotent to the first.

Analytical Methods

Analytical methods use numerical values equivalent to the module of the vectors.

Rectangular Components

Vectors are expressed as ordered pairs. The resultant vector is the sum of the respective rectangular components. If the vectors form a right angle, the result is determined using the Pythagorean theorem.

Orthogonal Components

These are the projections on the horizontal (X-axis) and vertical (Y-axis), defined according to fundamental trigonometric ratios, considering that any vector describes an angle to the horizontal:

Fx = F * cos(a)

Fy = F * sin(a)

Resultant: F = √(Fx² + Fy²)

Direction: tan(a) = Fy / Fx. If Fx is negative and Fy is positive, then the angle is in the 2nd quadrant.

A vector is used to represent a physical quantity which needs a magnitude and a direction (or orientation) to be defined.