There is actually a lot of strategy involved in whipping (once you actually learn what whipping is and the basics of how to do it, heh) For the record, its the button down on the bottom of the screen, that has an arrow pointing up (either lit or grayed out) that says "Hurry Production of XXX at the cost of Y populations, will cause ZZ turns of unhappiness".
Some key points I didnt realize when I first started playing:
1. There is a penalty for whipping items if there are no hammers in them
2. There is a penalty for whipping Wonders
3. Whipping 3 pop has the same unhappiness effect of whipping 1
Using proper technique, you can increase the effectiveness of whipping to avoid "wasting" potential hammers with penalties or having unhappiness pile up.
1. is the easiest. Try to avoid using the whip on items the first turn they are in the queue. This even applies if there is overflow hammers from the previous build, those hammers dont actually "go into" the next item until the following turn. They are sort of in limbo. Thats why an Archer takes 2 pop to whip. It costs 35 hammers to build an Archer on Epic speed, and you get 45 hammers per pop when whipping, but because of the penalty, you only get 30 (? I think) for the first one, then 45 for the second. If you put even 1 single hammer into the Archer, you can get him for 1 pop and still have some overflow.
Number 2 is probably my favorite way to build Wonders. You only get 30 hammers per pop on Epic if you whip the Wonder itself, but by putting a unit or building in front of the Wonder in the queue, you get the full 45 for whipping that item, and the overflow is applied into the Wonder at full value. You can actually pump out a respectable army using this technique. Say you are building the Mids, but want to get some Axes out to rush a neighbor. Put an Axeman in front of the Mids, let it build for a turn or 2, then whip to finish it. By carefully timing the whip, you can get a LOT of hammers into the Mids. Axemen are 52 hammers on Epic, so if your city is getting 17 hammers a turn, you can put 2 turns of 17 into the Axe, then whip it for 1 pop. You end up with 17 (first turn) + 17 (next turn) + 17 (actual finished turn) + 45 (1 pop whip) = 96 hammers for a 52 hammer build. That puts 44 hammers into the Mids, and gives you an Axeman.
3. Is a bit more painful, but if you have a city that grows REALLY fast and is constantly at the happy cap, but has very few hammer-tiles, you dont want to whip something for 1 then another something for 1 a few turns later, then another 1 a few turns after that. Unhappiness piles up and takes longer and longer to go away. I look for opportunities to whip for multiple pop, get plenty of overflow, and build bigger things much faster without a lot of actual hammers from tiles. By the time the city regains the population that extra frownie face is usually gone, or will be shortly.
Honestly, learning exactly how whipping and chopping hammers work and are applied to various things (trait bonus buildings, the bonus from OR, etc) has made me a much much better player.