Optimizing selects based on date functions.

[chastang]

Hello.
My question concerns a large data table that has a DATETIME column 
called dt. Specifically,  I am often having to do selects based on date 
and time functions that look like this:

select * from my_table where hour(dt)= 0
or
select * from my_table where month(dt) = 6
What index should I create to optimize selects on these sorts of 
queries? ["create index my_index on my_table(dt)" does not help.]

Thanks. -JC