Possible changes to rotational frequency of a quark inside a proton when special relativity is involved? Just think of the rotation of the quark inside a proton as the number of times it takes the highest position on an imaginary circle i.e. 90 degrees (up) to the center of mass of the proton. Now, let's push the proton to reach a relativistic speed. The quark must oscillate around the center of the proton and doing so it describes a path. If it collects the speed of the center of mass which is in relativistic translation (right direction) the quark has to add also the rotational part to its movement. From the FoR of the quark, the time is ticking slower but we look at it from the FoR of a stationary point. The path made by the quark should be like a helix (looking like a spring). So as the length of the helix is longer than the straight line made by the center of mass (CoM) of course the speed of the quark is greater than the speed of the CoM. So when CoM has speed 0.99c the quark has to have more than that. The rotational speed is a quantity that from the FoR of a stationary point should be the same but if the speed of the CoM increases the sum of these two velocities should not reach c. But it looks like it should be like so unless the rotational speed of the quark decreases.
 A: 
Just think of the rotation of the quark inside a proton as the number of times it takes the highest position on an imaginary circle i.e. 90 degrees (up) to the center of mass of the proton. Now, let's push the proton to reach a relativistic speed. The quark must oscillate around the center of the proton and doing so it describes a path. If it collects the speed of the center of mass which is in relativistic translation (right direction) the quark has to add also the rotational part to its movement. From the FoR of the quark, the time is ticking slower but we look at it from the FoR of a stationary point. The path made by the quark should be like a helix (looking like a spring). So as the length of the helix is longer than the straight line made by the center of mass (CoM) of course the speed of the quark is greater than the speed of the CoM. So when CoM has speed 0.99c the quark has to have more than that. The rotational speed is a quantity that from the FoR of a stationary point should be the same but if the speed of the CoM increases the sum of these two velocities should not reach c. But it looks like it should be like so unless the rotational speed of the quark decreases.

So we can conclude that the rotational speed of a linearly accelerated quark decreases.
Also rotational speed of a fan inside an accelerating spaceship decreases. And the rotational speed of a minute hand of an accelerated old-fashioned clock decreases.
We know how much the rotational speed of the clock hand decreases, don't we? At linear speed 0.87 it takes two minutes for the minute hand to make one round.
For simplicity's sake I have assumed that all rotations are transverse to the linear motion.
