Lorentz transformation and tilting of objects
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A meterstick is parallel to the x axis in S and is moving in the +y direction at constant speed vy. Show that the meterstick will appear tilted at an angle theta' with respect to the x'axis of S' moving in the +x direction at beta=0.65. Compute the angle theta' measured in S'.
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A detailed solution for the Lorentz Transformation and tilting of objects is provided.
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Consider the motion of the two ends of the meterstick. Let's label the coordinates of the ends by a subscript 1 or 2 to distinguish the two ends. In S we can take the spatial coordinates as a function of time of one end to be:
x1 = 0 and y1 = vy t
while the other end moves according to:
x2 = L and y2 = vy t
where L is the length of the meterstick.
Now, let's perform a Lorentz transformation to the frame S'. If S' moves in the x-direction according to x = v t, then a point with space-time coordinates p = (x,y,t) will correspond to the point with ...
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