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Home : Math & Science : Physics Study Guides : Special Relativity : Dynamics : Problems on Energy and Momentum
Problems on Four-vectors
Problem 2.1:
Find the inner product of the 4-momenta for the following two particles: a particle of mass m moving with
speed
![]() ![]() Problem 2.2:
Calculate the same inner product as in the previous question, but now in a frame moving with one of the
particles (or, if you already did it in such a frame, calculate it in the lab frame). Check that the result is the
same.
[Solution]
Problem 2.3:
Prove that if A and B are 4-vectors, A.B their inner product is independent of the frame in
which it is calculated.
[Solution]
Problem 2.4:
Derive the velocity addition formula using the invariance of the 4-velocity inner product. In other words, if in frame A, B moves to the right with speed v, and C moves to the left with speed u, find w, the speed of B with respect to C.
[Solution]
Problem 2.5:
Again using the invariance of the inner product, determine the speed of one particle as observed by the other
as two particles approach each other with speed v along trajectories separated by an angle 2θ,
as shown in the figure below.
![]()
Particle approaching each other at an angle.
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