The Moon moves at 14.685 arc-seconds per second. (The Earth spins at 15.04 arc-seconds per second ... but since the moon is orbiting as we spin, it makes the moon appear to move just fractionally slower than the stars.)
The formula for calculating field of view (assuming you have a calculator that works in Degrees) is:
Angular field of view = 2 * arctan(
sensor width / ( 2 *
focal length))
For an APS-C sensor camera (say 22.5mm in the horizontal direction) and a 600mm lens it's:
2 * arctan( 22.5 / ( 2 * 600))
This works out to a 2.148° field of view (in the horizontal direction)
Multiply that by 3600 to convert degrees into arc-seconds and that works out to 7732.8.
If I pick on my own Canon 60Da camera, the 18MP sensor is 5184 x 3456.
Divide 5184 / 7732.8 = .67 arc-seconds per pixel.
In 1 second, the moon will travel 14.685 arc-seconds. So 14.685 * .67 = 9.84 pixels (per second).
So if you were to take a photo of the moon at ISO 100, f/11, 1/100th sec (the "Looney 11" guideline)... it would move about .0984 pixels (you could just round that to .1 pixels) during that exposure (without a tracking mount).
This is why even though the moon does move ... you don't need to worry about it for purposes of most photography
By the way ... there is a total Lunar eclipse happening this Sunday night (Jan 20). It starts at roughly 9:30pm US Eastern time.
If you are photographing the moon during totality, the Looney 11 rule no longer applies (since the moon is no longer in full sunlight). This gets a bit more complicated. There is SIGNIFICANTLY less light on a fully-eclipsed moon. If you left the ISO and f-stop alone and only changed the shutter speed ... that 1/100th sec exposure when the moon isn't eclipsed could become a 30-minute exposure if the moon has a Danjon value of L=0 (darkest eclipse ... with the moon directly in the center of the shadow when the moon is near perigee.) At this weekend's eclipse... the moon WILL be at Perigee (which means it is closest to Earth). But it doesn't get to the very center of the shadow. Even a moderate totally eclipse could require 30 seconds to expose if you don't open up the aperture.
This would be a problem because if you require a 30 second exposure and the moon moves 9.84 pixels per second, the moon would move 295 pixels during that 30 second exposure if you don't have a tracking mount (that would certainly result in a smeared image.)
If you open up a couple of stops (say your 600mm lens can give you f/5.6) ... now the 30 second shot turns into an 8 second exposure. But then boost the ISO a few stops (say ISO 1600) and now you're down to a 1/2 second exposure (the moon will move about 5 pixels during that time). If your camera could handle ISO 3200 with acceptable results, now you're down to just a couple of pixels.
Keep in mind that 9.84 pixels per second is based on my own Canon 60Da astrophotography camera. I posted the math above so you can drop in your own focal length and your own sensor resolution to see how it applies to your own camera.
Anyway ... the best resource for eclipse photography is Fred Espenak (aka "Mr. Eclipse"):
How to Photograph a Lunar Eclipse