Republic of Cameroon
Peace-Work-Fatherland
The University of Bamenda
P.O.Box 39 Bambili
CA number 2
School: Fac Sci
Department: Physics
Option: Physics
Lecturers: Dr Mbakob
Course code: PHYS3244
Course title: Relativistic theories
Credit: 06
Date: 27/05/2023
Hall:
Time: 8am
Instructions: Submit on Wednesday before 10am
Duration: 4 days
Exercise 1
Use the velocity transformation formulas to derive the “particle aberration formula,”
Sin( )
tan( ') 
v

 (v)  Cos( )  
u

where the particle moves in frame S with a velocity u making an angle  with the x axis and the frame S’
moves in the x direction with velocity v, as usual, and the angle  ' is the corresponding angle in the frame
S’.
Exercise 2
Two particles are shot out simultaneously from a given point with equal speed u in orthogonal directions.
Show that the speed of each particle relative to the other is u 2 
u2
c2
Exercise 3
Two photons travel along the x axis of frame S with a constant distance d between them. Prove that
 v  v 
in frame S’ the distance between the photons is d 1  1   . (Hint: One approach is to
 c  c 
write the Doppler shift formula for the wavelength of light instead of its frequency.)
Exercise 4
1- Two particles move along the x axis at velocities 0.8c and 0.9c, respectively. The faster one is 1 m behind the
slower 1 at t=0. How many seconds elapse before they collide?
2- A rod of proper length 0.10 m moves longitudinally along the x axis of frame S at speed 0.50c. How long in frame
S does it take a particle moving oppositely at the same speed to pass the rod?
Exercise 5
A race car speeds past two markers spaced a distance 100 m apart in a time 0.04 ms as measured by an observer on the
ground.
1- How far apart are the markers as measured by the racer?
2- What time does the racer measure when he/she passes the second marker?
3- What speeds do the racer and observer on the ground measure?
Exercise 6
A rod with length of 1 m is inclined 450 in the xy-plane with respect to the x-axis. An observer with the
2
c approaches the rod in positive direction along the x-axis. How long does he seem the rod to be
3
and in which angle does he observe it to be inclined relative to his x-axis ?
speed
Courage dear all