How does paying extra principal on an ARM work?

[Joseph Henry]

I currently have a 30 yr fixed at 2.5%. Looking into buying a new primary home. With current rates, I am only thinking of a 5yr or 7yr arm. Never taken an ARM before. On a fixed mortgage, i could pay extra payments (or a one time lump sum payment) and apply it towards principal. This way, even if the monthly payment remains the same, the amount you pay towards principal each month goes up.

Does it work the same for an ARM. Any gotchas with ARMs?

[Joseph Henry]

Just to clarify, let's say the monthly payment is $5000 out of which $3000 goes to interest and $2000 goes towards principal. If I make a lump sum payment of $10,000 towards the principal, the future monthly payments of $5000 should go a lot more towards the principal since there is less total balance to calculate the interest. 

Is this correct even for an ARM?