length contraction

Examples of length contraction in the following topics:

• 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

  • Objects that are moving undergo a length contraction along the dimension of motion; this effect is only significant at relativistic speeds.
  • 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.
  • Length contraction arises due to the fact that the speed of light in a vacuum is constant in any frame of reference.
  • Consequently, the length of the ruler will appear to be shorter in your frame of reference (the phenomenon of length contraction occurred).
  • The effect of length contraction is negligible at everyday speeds and can be ignored for all regular purposes.

• Shifting the Paradigm of Physics

  • For example the length contraction formula is:
  • where $L_0$ is the rest length, the length of an object measured in the co-moving frame of the object, and $L$ is the length of the object as measured by the observer who sees the object moving at speed $v$.
  • In our rocket example, the stationary observer measures the length of the rocket as being less than what someone who was moving with the rocket would measure.
  • This altered the perception that the length of an object would appear the same regardless of the reference frame of the observer.
  • Thus in every day life $\gamma \approx 1$ and we do not experience significant time dilation or length contraction.

• The Speed of Light

  • For example, length contracts and time dilates (runs slower) for objects in motion.
  • The Lorentz factor (γ) is the factor by which length shortens and time dilates as a function of velocity (v):

• Surface Tension and Capillary Action

  • Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force.
  • This creates some internal pressure and forces liquid surfaces to contract to the minimal area.
  • Surface tension has the unit of force per unit length, or of energy per unit area.

• Volume Expansion

  • Substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions.
  • The volumetric thermal expansion coefficient is the most basic thermal expansion coefficient. illustrates that, in general, substances expand or contract when their temperature changes, with expansion or contraction occurring in all directions.
  • To derive the relationship, let's take a cube of steel that has sides of length L.
  • (a) Area increases because both length and width increase.

• Thermal Stresses

  • Railroad tracks and bridges, for example, have expansion joints to allow them to freely expand and contract with temperature changes .
  • To be more quantitative, the change in length ΔL is proportional to length L.
  • The dependence of thermal expansion on temperature, substance, and length is summarized in the equation
  • Thermal stress is created by thermal expansion or contraction.
  • Glass cooking pans will crack if cooled rapidly or unevenly, because of differential contraction and the stresses it creates.

• Linear Expansion

  • Materials which contract or maintain their shape with increasing temperature are rare.
  • To a first approximation, the change in length measurements of an object (linear dimension as opposed to, for example, volumetric dimension) due to thermal expansion is related to temperature change by a linear expansion coefficient.
  • It is the fractional change in length per degree of temperature change.
  • where L is a particular length measurement and dL/dT is the rate of change of that linear dimension per unit change in temperature.

• 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.