Let u = dr/dt be the velocity of a particle observed in an inertial frame K. The same quantity observed in an inertial frame K' moving with velocity v with respect to K is u' = dr'/dt'.
(a) Use the transformation properties of dt, r_ΙΙ, and r_⊥ directly to derive the velocity addition rule,

(b) Let v define a polar axis with polar coordinates u = (u, θ) and u' = (u', θ') for the particle velocities as measured in K and K'. Write the transformation laws in part (a) in the form u = u(u', θ') andθ = θ(u', θ').
(c) Use the results of (b) to show that u → c when ν → c.

Transcribed Image Text:

= dr dt = u + v v.u c² 1+ and U₁₁ = dr₁ dt U₁ (v)| 1+ v.u c²