Question 3: Transformation of Angles
In this question, you are asked to find and compare the transformations of the angle of the velocity vector of a particle and the angle of an inclined stick. The relationship between the two frames of reference is as usual.
(i) In frame S′, a stick makes an angle of θ′ with the x′ axis. What is the angle θ measured in the S frame. What is the length in the S frame?
(ii) Now we consider a particle moving with a velocity u′ in frame S′ at an angle θ′ to the x′ axis. Find the angle θ in the frame S.