From p=γumu (i.e., px=γumux,py=γumuy and pz=γumuz ), the relativistic velocity transformation (2-20), and the identity γu'=(1-uxv/c2)γvγu show that py'=py and pz'=pz.

Short Answer

Expert verified

It is shown that both frames’ y and z component momentum are equal by using the relativistic velocity and the given identity for γw'.

Step by step solution

01

 State the relativistic velocity transformation equations.

The relativistic velocity transformation between two frames S&S'is expressed as,

ux'=ux-v1-uxvc2

uy'=uyγr1-uxη3c2

uz'=uzyv1-uxvc2

02

Insert the above equations in the corresponding momentum equation.

The relativistic momentum in S'frame for the y-component is, py'=γumuy'

Inserting the expression for uy'and the given identity for γw'in the above equation,

py'=1-uxvc2γvγn(m)uyγv1-uxvc2

=γumuy

py'=py

Similarly, for the z-component in the frame S',

pz'=γummmuz'

=1-ucvc2γvγiu(m)uzγv1-uxvc2

=γumuz

pz'=pz

Thus, unlike relativistic x- component momentum, the y and z component momentum of both frames is equal.

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