Problem Imagine a wheel of radius [tex]R[/tex] consisting of an outer rim of length [tex]2\pi R[/tex] and a set of spokes of length [tex]R[/tex] connected to a central hub. If the wheel spins so fast that its rim is traveling at a significant fraction of [tex]c[/tex], the rim ought to contract to less than [tex]2\pi R[/tex] in length by length contraction, but the spokes ought not change their lengths at all (since they move perpendicular to their lengths). How do you think this problem is resolved? Solution Well, we know that there is no such thing on earth as a "rigid" body (ie, if we take a ladder and run into a wall, where the back of the ladder makes contact with the wall, we know that the front of the ladder keeps moving for a small amount of time, [tex]t < L/c[/tex] where [tex]L[/tex] is the length of the ladder since the front of the ladder has no way of "knowing" to stop (no information can travel faster than the speed of light). The same way, let us say that we start rotating the wheel with angular velocity [tex]\omega[/tex]. The outer rim doesn't start to move immediately... in fact, we will have turned the wheel a full [tex]L\omega / c[/tex] radians before the end of the wheel "knows" to start moving. Because of this, the spokes effectively shear slightly, reducing the velocity of the outer rim enough to account for the lessened circumference. Note that if we accelerate the wheel, this wouldn't apply to special relativity, since special relativity only deals with non-accelerating frames. [tex]\blacksquare[/tex] Is this a valid explanation? Also, how can we apply special relativity to this in the first place if an edge element of the wheel is considered to be accelerating? Should we consider the wheel to be extremely large such that the acceleration of each edge element, [tex]v^2/r[/tex], is very small, eliminating the need to use general relativity?