For focal plane blinds (the most common in DSLR), the blind is two curtains. The subject you should investigate is "focal plane shutter". One curtain over the sensor moves to open the exposure, and then the other moves to close it again. The exposure time is the delay between the two curtains.
The idea is that both curtains move in the same direction, so that all sensor areas receive the same exposure. Unlike any simpler leaf shutter, one opens and then simply closes again to the other side, so that one side of the sensor receives more light than the other side, which can be substantially more for a fast exposure time. For focal plane blinds, the sensor area is exposed equally, but not at the exact same time (since this open groove moves down in the frame).
And then, the synchronization of the shutter speed does NOT depend on any mechanical movement, but only depends on the delay of the second curtain. This delay is timed by a crystal, like any digital clock.
For a slow shutter speed, a curtain opens, stays fully open for a while, and a while later, the other curtain closes. The flash can only be fired when both curtains are fully open (called flash sync).
For a fast shutter, a curtain begins to open, and while it still moves and continues to open, the other curtain begins to close behind it. The actual exposure is then only the narrow "slit" width between the two curtains (a very fast shutter time in that slit). A quick flash cannot work in this narrow slot, it would not be synchronized to expose the full opening.
In your case, the speed of your curtain travel means that 1/180 seconds is the fastest possible shutter time that both curtains are fully open for flash. Faster, and the second curtain began to close, so that then, only a narrow "slit" would be exposed at a given moment by a quick flash.
Incidentally, a full-power flash is slower than 1/1000 seconds. That time is conventionally expressed as a time of t.5, that is, measured as the time between half of the power points, but there is much more light in the other half. A t.1 measurement (when the power is greater than 10%) is approximately three times longer. But the flash duration is measured conventionally at t.5 half power points. It is an engineering thing, measuring vague things that are difficult to know when it decays exactly to zero. But it is not exactly what photographers would like to know.
But, a flash means that the flash always fires at full power, and then the output is truncated or cut abruptly to perform any lower level, such as half power or 1/4 power. This means that the duration of the power levels below full power is more precise, more similar to t.1, but the total power is t.5. This is the reason why the specifications for half-power times and maximum flash power are approximately the same number, but with different meanings.
But regardless of that, for a focal plane shutter, both curtains must be fully open when any flash fires. The focal plane shutter is considered the best quality shutter, but it has this negative side of flash synchronization.