Come on, don't be shy. Explain the difference that 500g weight loss at the wheels will make in a 12 hour mountain bike race, Professor.
Consider the kinetic energy and "rotating mass" of a bicycle in order to examine the energy impacts of rotating versus non-rotating mass.
The translational kinetic energy of an object in motion is:
Where E is energy in joules, m is mass in kg, and v is velocity in meters per second. For a rotating mass (such as a wheel), the rotational kinetic energy is given by
where I is the moment of inertia, ω (pronunciation: omega) is the angular velocity in radians per second. For a wheel with all its mass at the outer edge (a fair approximation for a bicycle wheel), the moment of inertia is
Where r is the radius in meters
The angular velocity is related to the translational velocity and the radius of the tire. As long as there is no slipping
When a rotating mass is moving down the road, its total kinetic energy is the sum of its translational kinetic energy and its rotational kinetic energy:
Substituting for I and ω, we get
The r2 terms cancel, and we finally get
In other words, a mass on the tire has twice the kinetic energy of a non-rotating mass on the bike. There is a kernel of truth in the old saying that "A pound off the wheels = 2 pounds off the frame."
There you go, young grasshopper.