on the moment和in the moment都不用，和moment构成的短语常用的有：for a moment ；for the moment ；at the moment ；in a moment ；at any moment。
at the moment 意为“此刻”(与现在时连用)或“那时;当时”(与过去时连用).如:
I'm afraid I'm too busy at the moment to see anyone.
很遗憾,我此刻太忙,不能去见任何人。
2.for the moment意为“暂时”.如:
She is out,so you may use her typewriter for the moment.
她出去了,你可以暂时使用她的打字机。
3.in a moment 意为“立刻”.如:
I'll join you in the discussion in a moment.
我一会儿和你们一起讨论。
4.for a moment意为“一会儿”.如:
I had to think for a moment before I remembered his name.
我想了一会儿才记起他的名字。
5.at any moment 意为“随时”.如:
He told me I could call him at any moment.
他告诉我随时可以给他打电话。
