The issue of rotating vs. non-rotating mass came up in the Downtube thread. I posted about it in the Swift thread once. It's an interesting topic. I haven't found a thread devoted to it; why not in Folding Bikes?

I looked at this when James_Swift quoted the old saw about a pound of rotating weight being the same as a pound on the bike. I wasn't sure if I believed it, and did the following calculation:

The energy required to raise a mass M to a speed V is the familiar:

Et=0.5*M*V^2

The energy required to rotate an object with moment of inertia I to a rotaional rate omega is:

Er=0.5*I*omega^2

If the mass M is distributed at the radius R, the the moment of inertia is:

I=M*R^2

For a wheel moving forward at speed V, the rotation rate is:

omega=V/R

so Er=0.5*M*R^2*V^2/R^2=0.5*M*V^2

So a non-rotating mass requires energy

Et=0.5*M*V^2

While a rotating mass requires both the translational energy and the rotational energy to get up to speed.

Et+Er=0.5*M*V^2+0.5*M*V^2 = M*V^2; twice the non-rotating energy.

So, there is some truth to the pound of rotating = 2 pounds on the bike. I was a little surprised at the time that the result is independent of the radius of the wheel. Prior to the calculation I would have guessed that small wheels get a bit of a free ride.

This result only applies in accelerating the bike to speed. Once at speed, on a level road, you have to apply a torque to overcome the friction in the bearings (Edit: and rolling resistance and aerodynamic drag). That torque is not a function of the rotating mass. (Edit: What ultimatly limits your speed is mostly aerodynamic drag.)

So, while I agree in general that lighter is better than heavier, unless quick acceleration is critical for you, there's no particular reason to fuss over rotating vs non-rotating mass.

I know that there are other opinions out there!

Speedo