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1 - When no external forces act are both linear and angular momentum conserved in all 3 directions separately or just the total linear/angular momentum conserved ?

2 - if I approach a problem using conservation of both types of momentum can I use separate origins for linear and angular momentum or can i only use one origin per problem ?

3 - i have been looking at a problem when a cube slides on a frictionless surface and elasticly impacts on the bottom of a rod pivoted at its centre of mass. Using conservation of angular momentum and energy i can find the speed of the cube after the impact. But if i look at the problem using linear momentum i get( linear mom. of cube before) =( linear mom. of cube after impact) because the rod has no linear momentum because it centre of mass is fixed. This means the cube has the same speed after impact as before impact which i know is wrong. What am i doing wrong ?

Thanks