What you're asking about is at what shutter speed can you hand hold your camera. This is one of those questions that varies from person to person as to how steady you are.

But in answer to your question, yes, the magnification factor increases the shutter speed that would be safe to hand hold because it makes the lens a longer telephoto and more susceptible to vibration.

No. It's still a 90 mm lens, no matter the conversion factor. Actually, the next higher speed is usually 1/125th,
unless you have problems holding a camera steady.

Yes, the 90mm lens is still a 90mm lens, but any amount of shake is now a bigger percentage of the size of the smaller sensor, so for the rule of thumb of 1 over the focal length for a safe shutter speed needs to be adjusted for the conversion factor.

The rule of thumb is the equivalent lens on a 35mm camera. It is actually about angle of view, but expressed in 35mm focal length terms.

A 100mm lens on a digital camera with a 1.5x crop factor is equivalent to the angle of view 150mm lens on a 35mm camera. A 200mm lens on a medium format camera may be equivalent to a 100mm lens on a 35mm camera.

It is not about absolute focal length, but effective focal length expressed as its equivalency to a 35mm camera lens.

Larry,

Because you used the term "effective focal length" in your comments, there is another aspect no one has so far considered that needs to added to calculating a shutter speed relative to focal length. If for instance you are focusing on something much closer than infinity, especially with a longer lens the "effective focal length" increases quite substantially, and if your subject is very close the effect of camera movement on image can very easily result in blurring. This becomes quite obvious doing macro photography because at the same time you probably need a small lens aperture to obtain just a little depth of field. It's tripod time!

But let's take a more common situation, shooting handheld face close-up portraits with a 100mm lens and your subject is 5 to 10 feet away. Then, even with a full-frame camera the effective focal length is something between 125mm and 150mm, the with an APS dSLR with a 1.5X lens factor added, you really need to kick the shutter speed up for hand held shots, maybe to 1/250th second to be on the safe side.

I agree totally. The rule of thumb is not the absolute speed, but rather the minimum shutter speed of a camera held by the steady hand of a well practiced shooter, who is fully concentrating on holding as steady as possible. If one is less than steady, or casual about hand-holding, it is very easy to get a picture ruined by camera motion. It is photographic wisdom to use the highest possible shutter speed that circumstances permit, unless blur is part of the concept.

Resting ones hand against something solid for steadiness, leaning ones body against a wall, tree or whatever one can helps assure a lack of camera motion. A tripod, tabletop tripod or monopod is much better. Even when blur is part of the concept - panning with a race-car with a low shutter speed blurs the background and the car does not appear to just be parked on the track - is more easily done off a monopod, since it restrains the camera in the vertical axis, while permitting full freedom on the horizontal.

Cameras or lenses with anti-shake can make a great difference, though they don't address subject motion.

The rule of thumb does not deal with subject motion either - it is for a stationary subject. For action, much higher or lower shutter speeds may be necessary, since subject motion is now a far more important consideration than camera motion.

Shoot analysis is one of the most important fundamental skills in photography - understanding the circumstances and choosing the most appropriate equipment and settings to make optimum images within these circumstances.