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Relativistic Mechanics

Problem 1.365

The frame \(K^{\prime}\) moves with a constant velocity \(\mathbf{V}\) relative to the frame \(K .\) Find the acceleration \(w^{\prime}\) of a particle in the frame \(K^{\prime}\), if in the frame \(K\) this particle moves with a velocity \(v\) and acceleration \(w\) along a straight line (a) in the direction of the vector \(\mathbf{V}\); (b) perpendicular to the vector V.

Reveal Answer
 1.365. (a) w′=w(1−β2)3/2/(1−βv/c)3; (b) w′=w(1−β2) Here β=V/c.\begin{array}{l} \text { 1.365. (a) } w^{\prime}=w\left(1-\beta^{2}\right)^{3 / 2} /(1-\beta v / c)^{3} ; \text { (b) } w^{\prime}=w\left(1-\beta^{2}\right) \\ \text { Here } \beta=V / c . \end{array}
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