The following is junk science:
Dynamic friction on moving surfaces comes into play - I'd put $ on it that the 8kg has better quality components and therefore bearing than the 11kg bike..... Nothing to do with weight, but in cycling weight and quality is inextricably linked
Utter junk. Mechanical losses in a bike powertrain are tiny - and when you're running fast on the level most of the work is against air resistance, which means you only get the square root of the gain as a change in speed. So the difference between a pretty good bike and an excellent in this area will be something like the sqrt of 1.01...
Tires are another factor - I'm definitely faster on my light carbon fiber road bike than my heavy steel commuter bike, but the road bike has lightweight 23mm tires @ 110psi, compared with much heavier (puncture resistant) 32mm tires at 80psi on the commute bike so I suspect that most of the difference is in the wheels (and a more aerodynamic position on the road bike). – Johnny Oct 21 '13 at 19:51
Semi junk. The commuter bike may have higher RR tires, because a racer will be booted for speed and a commuter for puncture protection and tyre durability - but when tire design is the same, then wider is LOWER rolling resistance!
Stiffness also factors in. The stiffer the BB area, the less power lost to frame flex. How much, I couldn't say. But the reduction of mass for climbing, increased stiffness and reduced friction for increased power to the wheels combined probably add up to something noticeable
This too is junk. Yes, it's something that bike magazines tell you is a reason to buy their advertisers more expensive CF bikes. But lab tests haven't shown it. In fact, flexier frames can actually be faster especially in climbing - because the flex makes the frame act as a spring smoothing power transmission
...Super stiff bikes are excellent for elite sprinters, but for everyone else an expensive and uncomfortable waste of money.
The angular acceleration of your wheels is a factor as you are accelerating.
This is the worst junk. It's a factor, but an incredibly tiny one. Of all the stupid things cyclists believe about performance, the idea that wheel weight has a large effect is probably the stupidest because everyone has seen evidence to the contrary. When you work on your derailers and spin the pedals is there any great resitance to the wheel coming up to speed? No, it's instant. And if you wear a pair of leather gloves you can stop a wheel moving at the rpm for 20mph with a brush of your hands. Both these things are because the energy required to make the wheel spin are tiny. (There's a formula for this - you were supposed to have learned it in highschool!)
The worst case for a wheel is that it requires double the energy of non-rotating mass for kinetic energy. So for 2kg wheels, a 10kg frame and a 50kg rider, that's 4 to 10 to 50. The effects of wheel mass become even smaller when you consider a realistic case with resistive forces.