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.

\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}

Relativistic Mechanics