What is Length: Definition and 1000 Discussions

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.
Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in.
Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object.Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).

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  1. anemone

    MHB Length of Shortest Side In a Triangle

    If $a,\,b$ and $c$ are the sides of a triangle $ABC$, prove that if $a^2+b^2>5c^2$, then $c$ is the length of the shortest side.
  2. Uchida

    I Length Perception & Spacetime Warp: Is it Warped?

    If I make two rods with 1 meter length here on the surface of earth, and send one of them near a black hole that is at rest relative to earth, placing it there with its length alligned in the radial direction of the black hole, would I see the rod close to the black hole with a length shorter...
  3. G

    B Length Contraction Thought Experiment: Spot Mistake/Wrong Assumption

    Alice travels in a spaceship, which she measures to be L. The spaceship is moving with velocity v relatively to Bob. Alice makes a light beam traveling along the spaceship and measures the time interval it takes to go from one end to another, ΔtA. So, equation (1): L = c × ΔtA From Bob's...
  4. jeremiahrose99

    I Solution to the 1D wave equation for a finite length plane wave tube

    Hi there! This is my first post here - glad to be involved with what seems like a great community! I'm trying to understand the acoustics of a finite plane-wave tube terminated by arbitrary impedances at both ends. So far all of the treatments I've managed seem only to address a different...
  5. Tony Hau

    How to find the length of a vector expressed in polar coordinates?

    The velocity of a particle below is expressed in polar coordinates, with bases e r and e theta. I know that the length of a vector expressed in i,j,k is the square of its components. But here er and e theta are not i,j,k. Plus they are changing as well. Can someone help convince me that the...
  6. R

    B Is There a Connection Between Planck Length and Planck Time in Relativity?

    If Planck length is 10^-35 of a meter and Planck time is 10^-43 of a second, doesn't that mean that as the relative speed gets closer to the speed of light and time acceleration and length contraction are happening, they are happening at a different rate, since length contraction has to reach...
  7. alexm

    Motion of rotating rig, find the angle variation with control rod length

    Summary:: We have a rotating arm, offset from the centre of rotation by a certain length, which is controlled by varying the length of a control rod. Need the angle of the rotating arm in terms of length of the rod. The blue line is a fixed column structure. CE and BD form the rotational...
  8. George Keeling

    I Comparing Planck's Mass, Length, Time and Energy

    Sean Carroll gives the Planck's set of four dimensioned quantities: Planck's mass, length, time and energy. I wanted to compare them with actual things.\begin{align} m_p=\sqrt{\frac{\hbar c}{G}}&=2.18\times{10}^{-8}\rm{kg}&\rm{{10}^{7}\ E. coli}\phantom {100000000000000000000}&\phantom...
  9. D

    Length of a moment of eternity

    I have read a short story by the Grimm Brothers, named "The Sheperd Boy" and there is a riddle that sounds like this: So we have a mountain made of pure diamond, and it takes 1 hour to climb it, 1 hour to go around it and 1 hour to go down into it (I assume from its peak to its base). And...
  10. Adrian555

    A Geodesics of the 2-sphere in terms of the arc length

    I'm trying to evaluate the arc length between two points on a 2-sphere. The geodesic equation of a 2-sphere is: $$\cot(\theta)=\sqrt{\frac{1-K^2}{K^2}}\cdot \sin(\phi-\phi_{0})$$ According to this article:http://vixra.org/pdf/1404.0016v1.pdfthe arc length parameterization of the 2-sphere...
  11. Mikkel

    Python Numerical modeling of a glacier's length -- Coding error(s)

    Hey Physics Forum I am currently doing my bachelor project in geophysics, with focus on the evolution of glaciers in Greenland. My project consists partly of programming, because I want to get better at it. I have, however, hit a wall. I can't seem to figure out what is wrong with my code and I...
  12. B

    Balance length for a potentiometer circuit

    Here is the question itself Here is my attempt at it Does 4cm look right? Any help would be great, thanks!
  13. S

    Correct statement regarding the load vs length graph of a rubber band

    Option (B) is wrong because energy should be received by rubber band when it is being stretched Option (D) is wrong because energy should be released by rubber band when it goes back to natural length The area between graph of stretching and contracting represents energy dissipated in rubber...
  14. chriscarson

    How can you calculate change in length without force and area units?

    I have the STRESS , YOUNG S MODULUS ,and the LENGTH . How can you discover the CHANGE IN LENGTH when you don t have the FORCE and AREA unit ?
  15. chriscarson

    What is the Relationship Between Strain and Change in Length in Hooke's Law?

    Strain and change in length what is the difference ?
  16. chriscarson

    Young's modulus — Finding the change in the length of a metal bar under stress

    A steel bar 6.00 m long and with rectangular cross section of 5.00 cm x 2.50 cm supports a mass of 2000 kg. How much is the bar stretched ? (the young s modulus of steel is 20 x 10 n\m squared)
  17. P

    Understanding Gauss's Law in Cylindrical Shells of Non-Infinite Length

    My question is going to be rather specific. I am trying to understand how Gauss's law applies to this scenario. I know if a cylindrical shell is infinitely long, and there is an external electric field, the inside of the shell will have an electric field of zero everywhere. I am wondering...
  18. Charlie Cheap

    Automotive Spark length of a points ignition compared to an HEI system

    Having made/modified my own distributors for years, I was surprised to see MSD (Multiple Spark Discharge) company show their graph using Points, HEI, and Performance HEI comparisons, with little difference in Horse Power made, up to about 6000 RPM. I know a points mechanical system makes a...
  19. Saracen Rue

    I How to find the maximum arc length of this equation?

    After seeing a discussion about graphs of the relationship ##x^x + y^y = r^r##, it got me interested in attempting to see what the graphical appearance of ##{^{\infty}x}+{^{\infty}y}={^{\infty}r}## would look like. The first step I did was use the relationship of...
  20. Edwin1974

    I True length of sidereal year in 6000 b.c.e.

    Hi there :smile: Anybody out there able to explain to me how to calculate what the true length of a sidereal year was about 6000 years ago ? Kind Regards Edwin.
  21. M

    B Help! Solving Einstein's Length Contraction Problem

    I have to admit that my "best" math days are long gone. That said, I wonder if anyone can help me? I'm stuck in part 1 of Einstein's book on 'Relativity, The Special & General Theory: The behaviour of measuring rods & clocks in motion', specifically on the second equation : √(1-v^2/c^2) used to...
  22. marielescobal

    Calculation of bond length using Raman spectra

    Hi, I really need your help. Suppose I have a Raman spectra of a hydroxyapatite, how do I calculate the bond length from the spectra? I've been trying to understand the concept of Badger's rule but I really cannot understand. Please help.
  23. jnorman34

    I Planck Length & Singularity: Point or Sphere?

    Since Planck length is a distance unit of space-time which cannot be further subdivided, would that not imply that an electron, or singularity, or any other point particle cannot actually be a “point”, but must rather be a spherical volume with a Planck length diameter? i realize this may well...
  24. G

    MHB Calculate the length of the fourth side edge.

    The three lateral edges of a pyramid based on a square are 6016, 2370 and 4350 long. Calculate the length of the fourth lateral edge. We assume that edges 6016 and 2370 extend from the opposite tops of the base.
  25. C

    Optics focal length and optical power Question

    1/f = 1/dₒ + 1/dᵢ = 1/1.0 + 1/0.33 = 4.03 m (focal length) Power: 1/4.03 m or 0.248 (0.25) *around to the2 decimal points? or leave it as a fraction? ((Did I do this correctly? I am not sure if this is correct and is it okay to be in meters not centimeters?)) Please let me know!
  26. O

    Diffraction pattern due to a lens with focal length f

    Suppose one light up with a laser on a grid with grid constant g. The grating is followed by a focusing lens with a focal length of f. In the focus (or immediately in front of it) the maxima have a distance d. How large was the distance of the maxima immediately after the grating? scheme: Laser...
  27. M

    Draw and find the Length of x=t+4 , y=t2+1

    Hi, my try: Do you agree with me? Thanks
  28. B

    Length of a string over a 2 pulley system

    Hello all, I am working on a lab report for physics, and am a bit stuck on one aspect. The basic layout of the pulley system is attached. (This is a diagram I made, so if there are any inaccuracies in this one either, I am happy to fix it. So, I mostly understand the lab. My TA said, though...
  29. B

    Determining Radiation Length in Air

    The radiaton length for air is about $$X_0 = 30420cm$$. This is the length at which the electron has decreased to 1/e of it´ s initially value. I also know that the maximal value of interactions for a specific energy is given by $$ n_{max} = \frac{ln(\frac{E_0}{E_c})}{ln(2)} $$, where E_c is...
  30. N

    B Clarification on Length Contraction

    The rule for length contraction seems to be inconsistent with the lorentz transformations for distance. The rule for length contraction is: ## x = \gamma x ^\prime ## and ## x ^\prime = \frac {1} {\gamma} x ## But the lorentz transformations for distance are ## x = \gamma x ^\prime + \gamma vt...
  31. B

    Propagation of Error for Focal Length

    Homework Statement: Propagation of Error for Focal Length Homework Equations: f = (s'*s) / (s' + s) In my lab, we had to calculate the focal length of a lens based on object distances (s) and image distances (s') that we measured. The object distances were measured with an uncertainty of...
  32. B

    I Time Dilation, Length Contraction & Massive Bodies

    For instance, if a stream of muons were released from a box near a massive object and traveled on a straight path slowly (at a non-relativistic velocity) away from that object, a faraway observer would notice that the particles would take longer to decay than a muon typically would in empty...
  33. S

    B Length Contraction in Accelerated Frame

    I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis. I was looking a this paper for clarification.
  34. Z

    Switching speed of ICs vs gate length

    Why is it that the smaller the gate length, the higher the max operating frequency becomes? In particular, I think I saw somewhere that a 6 um gate length, seems to limit ICs to 100kHz, where as 1 um is around 1MHz (all rough ball bark numbers, and can be persuaded otherwise). Was wondering if...
  35. D

    Physical optics -- counting interfence fringes to measure a length change

  36. A

    I How time dilation is a permanent change and length contraction not?

    Comparing high precision atomic clocks, one flying in a airplane and one on the ground had demonstrated permanent time dilation presumably due to special relativity (speed) and/or general relativity (gravity) . While similar experiment with a ruler would demonstrate length contraction only...
  37. ColdheartedGod

    B Schwarzschild radius of an object is smaller than Planck length

    I had this idea when some people said that LHC can produce black hole. Based on the calculation of Schwarzschild Radius, any mass than 9.375×10^7 kg have a Schwarzschild radius smaller than the plank length. Particles inside LHC or other particle accelerator have clearly radii smaller than that...
  38. Telemachus

    Magnetostatics and Ampere's law on a finite length wire

    I tried to think why Ampere's law seems to fail in this case. For me it was clear that there is no symmetry in the z direction, there is no translational symmetry because of the finiteness of the wire. On the other hand, I know that Ampere's law is independent of the loop we take. This also...
  39. U

    Understanding the Math Behind A: Minimum Length of Plane Mirror

    15. What is the minimum length of a plane mirror in order for you to see a full view of yourself? A 1/2 your height B 1/4 your height C 3/4 your height D your full height Q Why is answer of A given is the correct one, I understand pictorially how it is, since visually if you were to draw a...
  40. S

    B Can a wavelength be smaller than a Planck length?

    According to this article https://physics.stackexchange.com/questions/321229/why-dont-we-have-proton-neutron-microscopes, they seem to hint that heavier objects have a shorter wavelengths and give better resolution. If I kept increasing the mass of a particle and kept it's speed at .9c would I...
  41. DaTario

    A Increase of coherent length in stimulated emission

    Hi All, When I teach the basic structure of a laser setup, stimulated emission appears as a fundamental phenomenon. But in no reference I found a description that could account for the increase of coherent length of the EM laser field. According to my knowledge, one photon typically doesn't...
  42. D

    Help with Length contraction of ruler at 60degree angle to observer

  43. M

    Helicoidal movement: acceleration vector, arc length, radius of curvature

    I have tried to solve it and I would like a confirmation, correction or if something else is suggested... :) Helicoidal movement
  44. M

    I Length Contraction & FTL Speeds: Are Lower Grades Faster?

    I’m not a physicist but let’s say hypothetically ;we have the Millennium Falcon. It’s FTL hyperdrive can go Class 0.5 past lightspeed. Then we have an X-wing which has a Class 1 past lightspeed drive. This is all from the lore. MF is 0.5 and X Wing is 1 but MF is faster. Anyway even though the...
  45. U

    Finding the Length of a wire

    How to find the length of a wire of a 3000 Kelvin incandescent light bulb that produces L = 60W of power. The diameter of the wire is 0.00005m. I'm quite confused, as the resistivity of the bulb isn't given so I'm not sure what equation to use as resistivity = resistance × area / length does...
  46. F

    I Light pulse path, length and shape, when bouncing between two mirrors

    Hello, A light pulse moving bouncing between two mirrors (top and bottom) follows a vertical straight path w.r.t. to an inertial observer at rest relative to the mirrors. However, a moving inertial observer see the light pulse move in a zig-zag path as it bounced back and forth between the...
  47. M

    Fluids and low-g length scale

    Hi PF! Fluids in low gravity have a natural oscillation frequency ##\lambda = \sqrt{\sigma / (\rho L^3)}##, where ##\sigma## is surface tension, ##\rho## density, ##L## characteristic length. Then given a particular object, say a sphere, is ##L=D## or ##L=r##? How about a channel; would ##L##...
  48. jisbon

    Conservation of Energy and change in the length of a spring

    Hola! So my first approach to this is use both the conservation of energy and momentum equations since collision between the first two objects are elastic. Let the 3 blocks be a,b and c (from left to right) Does this means the following: whereby ##v_{a} ##= speed of block a after collision...
  49. C

    I "Spatial Width," "Coherence Length," and the Measurement Problem

    A new (short 3 pg) paper, making quite a grandiose claim, caught my eye last night: https://arxiv.org/abs/1908.07719 Abstract: We propose an experiment of two-path interference in which the optical path difference between the two interferometer arms is much larger than the spatial spread of...
  50. S

    Huge pressure drop after changing pipe length (Don't think it's loss)

    Hi All, Recently, I have been struggling to seek a solution for a seemingly simple flow question and try to rationalize my thoughts with mechanical engineering knowledge I have acquired from school but none of them can make me feel comfortable about answering the phenomenon I encountered in...
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