We use cookies to ensure you get the best experience on our website. By using the IFPA wiki, you consent to our use of cookies.


From IFPA wiki
  1. Are there nonlinear symmetries in Newton's equations?
  2. Show that, in the case of a [math]k/|{\overrightarrow r}|[/math] potential, there is an extra conserved quantity: the Laplace–Runge–Lenz vector [math]{\overrightarrow A}={\overrightarrow P}\times {\overrightarrow L}-mk{{\overrightarrow r}\over |\overrightarrow r|}[/math].
  3. A spaceship travels to a star 8 light-years away, in a time its crue considers to be 8 years. What speed does the ship travel at?
  4. Frame S is at rest, frame S' has velocity v' w.r.t. S, and frame S" has velocity v" w.r.t. S'. What is the velocity of S" w.r.t. S'? Work this out using hyperbolic coordinates [math]v/c=tanh(\chi)[/math] and show that the [math]\chi[/math]'s are additive.
  5. In a distant galaxy, hydrogen emits microwaves of wavelength 21 cm. These are observed on Earth to have a frequency of 1.2 GHz. How fast is the galaxy receding from Earth?
  6. A rod of length L moves with speed v along the x' axis. In its rest frame, the rod makes an angle θ' with respect to the x' axis.
    1. Determine the length of the rod as measured by a stationary observer.
    2. Determine the angle θ that the rod makes with the x axis, assumed parallel to the x' axis, in the stationary frame.



IFPA Wiki maintained by Atri B.

ULgLogo.png     Logo-star.png