1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Components of the 4-acceleration

  1. Nov 25, 2007 #1
    1. The problem statement, all variables and given/known data

    I read in my textbook that "in the instantanuous reference frame (IRF) [tex][u^{'\gamma}]=(c,\overline{0}) [/tex] imply that the components of the 4-acceleration in the IRF are [tex] [a^{'\gamma}]=(0,\overline{a'}) [/tex]"

    2. Relevant equations

    3. The attempt at a solution
    I don't know why they got a' for the space-like components of the 4-acceleration. Isn't the accelaration = du/d[tex]\tau[/tex] if so then using [tex][u^{'\gamma}=(c,\overline{0}) [/tex] we get zero for both the time-like and space-like components of the 4-acceleration.
    Last edited: Nov 25, 2007
  2. jcsd
  3. Nov 26, 2007 #2

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Think back to first-year calculus, and suppose [itex]f\left(x\right) = x^3[/itex]. Then, [itex]f\left(2\right) = 8[/itex], and [itex]8[/itex] is a constant, so

    [tex]\frac{d}{dx}8 = 0,[/tex]


    [tex]\frac{df}{dx}\left(2) = 12 \ne 0.[/tex]

    Just because the 4-velocity has a particular value (which could have zero spatial part) in a particular frame at a particular instant doesn't mean that the 4-velocity is constant. If the 4-velocity is not constant, then the 4-acceleration doesn't have to be zero.

    Throw a ball in the air. When the ball reaches its greatest height, its (spatial) velocity is zero, but its (spatial) acceleration still has magnitude [itex]g[/itex]
  4. Nov 26, 2007 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In addition, note that the 4-acceleration of a particle is orthogonal to its 4-velocity. (Why?)
    Last edited: Nov 26, 2007
  5. Nov 27, 2007 #4
    That example was very helpful. thanks a lot.

    Thanks robphy too.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook