magnitude

(noun)

A number assigned to a vector indicating its length.

Related Terms

Examples of magnitude in the following topics:

  • Multiplying Vectors by a Scalar

    • Multiplying a vector by a scalar changes the magnitude of the vector but not the direction.
    • To multiply a vector by a scalar, simply multiply the similar components, that is, the vector's magnitude by the scalar's magnitude.
    • This will result in a new vector with the same direction but the product of the two magnitudes.
    • For example, if you have a vector A with a certain magnitude and direction, multiplying it by a scalar a with magnitude 0.5 will give a new vector with a magnitude of half the original.
    • The force is a vector with its magnitude depending on the scalar known as mass and its direction being down.

  • Scalars vs. Vectors

    • Vectors require two pieces of information: the magnitude and direction .
    • In contrast, scalars require only the magnitude.
    • Vectors require both a magnitude and a direction.
    • The magnitude of a vector is a number for comparing one vector to another.
    • The greater the magnitude, the longer the arrow.

  • Order of Magnitude Calculations

    • Such differences in order of magnitude can be measured on the logarithmic scale in "decades," or factors of ten.
    • The order of magnitude of a physical quantity is its magnitude in powers of ten when the physical quantity is expressed in powers of ten with one digit to the left of the decimal.
    • Orders of magnitude are generally used to make very approximate comparisons and reflect very large differences.
    • If two numbers differ by one order of magnitude, one is about ten times larger than the other.
    • If they differ by two orders of magnitude, they differ by a factor of about 100.

  • Forces in Two Dimensions

    • For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result.
    • In this simple one-dimensional example, without knowing the direction of the forces it is impossible to decide whether the net force is the result of adding the two force magnitudes or subtracting one from the other.
    • The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action.
    • Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can be done to determine the net force.
    • Forces are resolved and added together to determine their magnitudes and the net force.

  • Introduction to Scalars and Vectors

    • A vector is any quantity that has both magnitude and direction, whereas a scalar has only magnitude.
    • It does not change at all with direction changes; therefore, it has magnitude only.
    • Whereas displacement is defined by both direction and magnitude, distance is defined by magnitude alone.
    • A vector is any quantity with both magnitude and direction.
    • It is any quantity that can be expressed by a single number and has a magnitude, but no direction.

  • An Astronomical Aside: Magnitudes

    • Astronomers typically speak about the flux of an object in terms of magnitudes.
    • A magnitude is generally defined as
    • Pogson empirically determined the value of "2.5" by comparing the magnitudes of prominent observers of the 1800's.
    • It is remarkably close to $\ln 10 \approx 2.3$, so a change in magnitude of 0.1 is about a ten-percent change in flux.
    • If $g(\nu) = 1$, the quantity is called a "bolometric magnitude."

  • A Practical Aside - Orders of Magnitude

    • One of the most important tools that a card-carrying astrophysics has is the order of magnitude estimate.
    • The order of magnitude estimate combines the lack of rigor of dimensional analysis with the lack of accuracy of keeping track of only the exponents; this makes multiplication in your head easier!

  • Components of a Vector

    • Vectors are geometric representations of magnitude and direction and can be expressed as arrows in two or three dimensions.
    • Vectors are geometric representations of magnitude and direction which are often represented by straight arrows, starting at one point on a coordinate axis and ending at a different point.
    • All vectors have a length, called the magnitude, which represents some quality of interest so that the vector may be compared to another vector.
    • A vector is defined by its magnitude and its orientation with respect to a set of coordinates.
    • For three dimensional vectors, the magnitude component is the same, but the direction component is expressed in terms of $x$, $y$ and $z$.

  • Unit Vectors and Multiplication by a Scalar

    • Multiplying a vector by a scalar is the same as multiplying its magnitude by a number.
    • Scalars are distinct from vectors in that they are represented by a magnitude but no direction.
    • When multiplying a vector by a scalar, the direction of the vector is unchanged and the magnitude is multiplied by the magnitude of the scalar .
    • A unit vector is a vector with a length or magnitude of one.

  • Position, Displacement, Velocity, and Acceleration as Vectors

    • Vectors are a combination of magnitude and direction, and are drawn as arrows.
    • The length represents the magnitude and the direction of that quantity is the direction in which the vector is pointing.
    • When the inverse of the scale is multiplied by the drawn magnitude, it should equal the actual magnitude.
    • Velocity is also defined in terms of a magnitude and direction.
    • In drawing the vector, the magnitude is only important as a way to compare two vectors of the same units.