Sometimes in bright backlight and with large aperture (f2.8) I want flash at high shutter speeds. But when I pop the flash up on D7000 it caps the shutter speed to 1/250th, which overexposes the shots and makes everything look like a nuclear bomb just went off.
What's the logic behind the limiting of the shutter speed when using flash? Is there anything I can do to get flash + faster shutter speeds?
The limitation has to do with synchronizing the length of the exposure with the length of the flash burst. The flash does not go off immediately...it occurs a fraction of a moment after the shutter has opened, and the burst only lasts a fraction of the time the shutter is open. This is necessary to produce a proper exposure when using a full-powered flash due to the way the shutter itself works. The maximum shutter speed that can be achieved at is 1/200th or 1/250th of a second most of the time. With more precise logic and shutter timing, you can achieve 1/500th of a second flash sync, however thats more difficult (and therefor expensive) to do, which is why its relegated to only top of the line pro-grade cameras. This ensures that the front shutter curtain is fully open before the flash pulse is set off, and that it stays open long enough for the effects of flash to properly light the scene and allow correct exposure before the second curtain closes.
There is also an alternative approach to flash, called high-speed flash sync. This allows flash to be used at any shutter speed. The difference between high speed flash sync and normal flash sync is that at shutter speeds above about 1/500th of a second, the second curtain starts to close before the first curtain is fully open...a shutter "gap" transitions across the sensor. High speed flash sync uses a lower-powered flash pulse set off multiple times in rapid succession to ensure that the scene is properly lit for each part of the sensor as that shutter gap moves across it. High speed flash sync is generally not as good as standard flash, and in most cases it should not be needed...but in a pinch it can do the job.
Most dSLRS use focal plane shutters with two curtains. The first curtain "opens" the shutter, and the second one "closes" it. The size of the gap between the two shutters determines the shutter speed. The smaller the gap, the faster your shutter speed. When you reach your maximum sync speed (usually around 1/200s, for most cameras), that's the fastest shutter speed where the whole sensor is uncovered by the gap between the curtains. Once you go faster than that, the gap between the curtains is smaller than the sensor.
The light pulse from a flash, however, is likely to be much faster than your shutter speed. And if you use a faster shutter speed, then either the top or bottom (or both) of the sensor will be covered by a curtain while the flash burst goes off. So you'll get dark bars at the top or bottom (or both) of the frame. Since most people don't want this, the camera will automatically limit the shutter speed to the maximum sync speed with flash.
There is a feature called high-speed sync (HSS) or focal plane (FP) flash, which can get the shutter synchronization and multiple pulses from the flash so that the entire sensor will be evenly illuminated for the length of the exposure, but this requires more sophisticated communication between the flash and the camera, and most built-in "pop-up" flashes cannot perform HSS. And you typically need a TTL-capable hotshoe flash to do this (although not all TTL-compatible flashes can do HSS, either. OEM (same brand as your camera) flashes are your best bet). Be aware, however, that HSS will lower the effective power and light output of the flash by roughly two stops.
See: Neil van Niekerk's tutorial on HSS, for more detailed information.
After Jristas excelent answer I was interested to learn more as the exlaination was more complicated that I had anticipated.
Both these articles give very detailed explainations:
tutorial: high-speed flash sync
maximum-flash-sync-speed
Worth mentioning that High Speed Sync (HSS) on Nikons including the D7000 is refered to as "Auto FP". This can be set on the D7000 via:
menu -> Custom Settings Menu -> e Bracketing/flash -> Flash sync speed.
