Originally Posted by
Jaywalk3r
The spokes do not extend the ground, nor to the center of the axle, and those are the only two points along the wheel assembly's radius at which the linear speed will be the same for the spokes of different size wheels. Everywhere else, which is the entire length of the spoke on actual wheels, the linear speeds are different.
My reasoning was incorrect. It's not clear whether, all else equal, the linear speed of the spokes of the smaller wheel would be faster or slower.
The spokes would have the same linear speed at corresponding points along the spoke lengths, assuming the same bicycle speed, if the wheel assemblies were proportionally identical. In other words, the larger wheel would have to also have a proportionally larger hub and a proportionally taller tire. With all else equal, the smaller wheel has a proportionally larger hub and a proportionally larger tire & rim. The two factors result in opposite, but not necessarily equal, effects on the linear speed of the spokes.