Are there any exciting experiments for the conservation of linear momentum?
Lots... www.fnal.gov/ www.cern.ch/ www.slac.stanford.edu/
Is there something particular you are looking for?
Experimetns that can be done at home or in a school lab
You probably don't need to full machinery of special and general relativity for the experiments described below:
You could study the collision of billiard balls
or the ballistic pendulum http://hyperphysics.phy-astr.gsu.edu/Hbase/balpen.html
or Newton's Cradle http://www.lhup.edu/~dsimanek/scenario/cradle.htm
or carts on a track http://www.physics.ucla.edu/demoweb/demomanual/mechanics/second_law/dynamic_track_demos.html
or many more: http://www.google.com/search?q=conservation+of+momentum+lab
Hmm, I guess that rules out the hunting rifle I was going to suggest
Thanxx guys for all your help!!! the Rifle one souds great
However are there no experiments that has a step by step method and an apparatus...?
Separate names with a comma.