Length

(noun)

How far apart objects are physically.

Examples of Length in the following topics:

  • Length

    • Length is one of the basic dimensions used to measure an object.
    • In other contexts "length" is the measured dimension of an object.
    • Length is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).
    • In the physical sciences and engineering, when one speaks of "units of length", the word "length" is synonymous with "distance".
    • There are several units that are used to measure length.

  • Length

    • Length is a physical measurement of distance that is fundamentally measured in the SI unit of a meter.
    • Length can be defined as a measurement of the physical quantity of distance.
    • Many qualitative observations fundamental to physics are commonly described using the measurement of length.
    • Many different units of length are used around the world.
    • The basic unit of length as identified by the International System of Units (SI) is the meter.

  • Length Contraction

    • Let's look at the results with the aether again.If we have a rod of length $L_0$ in the primed frame what it is length in the unprimed frame.
    • We have define the length to be the extent of an object measured at a particular time.

  • Length Contraction

    • Length contraction is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer.
    • Now let us imagine that we want to measure the length of a ruler.
    • Consequently, the length of the ruler will appear to be shorter in your frame of reference (the phenomenon of length contraction occurred).
    • For example, at a speed of 13,400,000 m/s (30 million mph, .0447c), the length is 99.9 percent of the length at rest; at a speed of 42,300,000 m/s (95 million mph, 0.141c), the length is still 99 percent.
    • Observed length of an object at rest and at different speeds

  • Stress and Strain

    • The ratio of force to area $\frac{F}{A}$ is called stress and the ratio of change in length to length $\frac{\Delta L}{L}$ is called the strain.
    • In equation form, Hooke's law is given by $F = k \cdot \Delta L$ where $\Delta L$ is the change in length and $k$ is a constant which depends on the material properties of the object.
    • Deformations come in several types: changes in length (tension and compression), sideways shear (stress), and changes in volume.
    • The ratio of force to area $\frac{F}{A}$ is called stress and the ratio of change in length to length $\frac{\Delta L}{L}$ is called the strain.
    • Tension: The rod is stretched a length $\Delta L$ when a force is applied parallel to its length.

  • Elasticity, Stress, and Strain

    • In equation form, Hooke's law is given by $F = k \Delta L$ , where $\Delta L$ is the change in length.
    • Strain is the change in length divided by the original length of the object.
    • Experiments have shown that the change in length (ΔL) depends on only a few variables.
    • Additionally, the change in length is proportional to the original length L0 and inversely proportional to the cross-sectional area of the wire or rod.
    • Tension: The rod is stretched a length ΔL when a force is applied parallel to its length.

  • The Lensmaker's Equation

    • The lensmaker's formula is used to relate the radii of curvature, the thickness, the refractive index, and the focal length of a thick lens.
    • The focal length of a thick lens in air can be calculated from the lensmaker's equation:
    • The focal length f is positive for converging lenses, and negative for diverging lenses.
    • The reciprocal of the focal length, 1/f, is the optical of the lens.
    • If the focal length is in meters, this gives the optical power in diopters (inverse meters).

  • Combinations of Lenses

    • The simplest case is where lenses are placed in contact: if the lenses of focal lengths f1 and f2 are "thin", the combined focal length f of the lenses is given by
    • If two thin lenses are separated in air by some distance d (where d is smaller than the focal length of the first lens), the focal length for the combined system is given by
    • If the separation distance is equal to the sum of the focal lengths (d = f1+f2), the combined focal length and BFL are infinite.
    • The magnification can be found by dividing the focal length of the objective lens by the focal length of the eyepiece.
    • Calculate focal length for a compound lens from the focal lengths of simple lenses

  • Angular Position, Theta

    • We define the rotation angle$\Delta \theta$ to be the ratio of the arc length to the radius of curvature:
    • The arc length Δs is the distance traveled along a circular path. r is the radius of curvature of the circular path.
    • We know that for one complete revolution, the arc length is the circumference of a circle of radius r.
    • The arc length Δs is described on the circumference.

  • Unit Vectors and Multiplication by a Scalar

    • This results in a new vector arrow pointing in the same direction as the old one but with a longer or shorter length.
    • A unit vector is a vector with a length or magnitude of one.
    • This can be seen by taking all the possible vectors of length one at all the possible angles in this coordinate system and placing them on the coordinates.
    • (i) Multiplying the vector A by 0.5 halves its length.
    • (ii) Multiplying the vector A by 3 triples its length.