[bob1029]

10000g peak forces are a bit of a mess for space travel.

Perhaps instead of directly spinning the object up to speed and "letting go", you could build up all of the energy into a heavy rotating mass which then imparts it into the spacecraft over a slightly longer timeframe via some simple mechanical clutch and cable arrangement. You would still have very strong g-forces, but you could control the impulse curve over time to spread out the forces better.

Steel cables, flywheels and other members aren't going to care about such forces as much as the delicate electronics on board a spacecraft. Let these parts do the heavy lifting and then transmit the energy into the spacecraft in a methodical manner. You need to decouple the extreme nature of this sort of energy storage system from the spacecraft until it is go time.

[londons_explore]

You very quickly get to multi-kilometer ropes, and the need to accelerate a far higher mass than the launch mass...

[craftinator]

Reminds me of Seveneves by Neal Stephenson. In a future setting, they use long whip like objects to fling objects around in space, with a flywheel to drive them.