Another one of my visual metaphors for beginners is to help give them a little more momentum across the dojo. Beginners tend to forget that there's a fair whack of weight in a shinai, especially once you've set it in motion. I think they feel a need to wrestle with it once they've committed it from jodan [or that position half way down their back they think is jodan ;) ], to feel like they are holding it as they cut, and so forget that all that tension is eventually going to be transferred to their aite's head.
I'm not sure at what point I made this connection but I think it was coincidentally around the now infamous example my Sensei presented to all about the momentum of a shinai. He stood at one end of the dojo and cut but did not hold onto the tsuka - the shinai sailed practically the entire length of the dojo before smacking dead centre in the floor to ceiling mirrors on the far side. The point being that you can use that momentum to pull you across the dojo. Instead of fighting it, embrace it and go with it and when you add in that rear wheel drive from your left foot you can really pick up pace across the dojo.
So the image you really need to get into your head is exactly what happens to Tom Cat in this classic Tom and Jerry cartoon at 4:32 you can see what happens to Tom when he makes his 'downswing'. He ends up on the other side of the bowling alley. So the next time you go and cut men try letting the shinai take you with it.
Once again you may choose to disregard any or all of my opinion but I think for your average beginner this is decent advice. So long as you remember a bit of tenouchi at the end and if you are cutting correctly the tip is going out and not down; otherwise in Sensei's example his shinai would have hit the ground a few feet in front of him then skittered across the floor in any old direction.
So throw it out with a loose grip, catch it at the point of contact with tenouchi and use it's momentum to pull you across the dojo, just like Tom Cat