= Relativistic force transformation
{title2=$F_\perp=F'_\perp/\gamma$}
= Force transformation
{synonym}
For a particle instantaneously at rest in a primed frame moving at $v\widehat{\mathbf x}$ relative to the laboratory, the ordinary three-force transforms as $F_\parallel=F'_\parallel$ and $F_\perp=F'_\perp/\gamma$. The spatial components of the <four-force> are $\gamma_u\mathbf F$, whereas its time component is $\gamma_u\mathbf F\cdot\mathbf u/c$. For a co-moving material segment, <length contraction> also changes its laboratory length, so transforming total force is not the same as transforming <force per unit length>.
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