Veritasium explains why we cannot have now a contraption, a device, that is going to have the speed of light: because we do not have such freaking big amounts of energy, that is why.
If you were to have a stick long enough to reach the Moon and would move it fast over the Moon’s surface so that it may appear that the tip of the stick is moving faster than the speed of light, then that would not be possible. Why? Because the fastest a force can move through the stick from your hand to the tip of it is the speed of sound in that stick (remember the slinky experiment).
But if you were to have a rotating satellite that rotates at over 10000 rpm and has two long arms of 285 km each, then the tips of those arms wouldn’t have the speed of light? Nope. Because of the relation between the centripetal force and the arms speed. The centripetal acceleration is ac = v^2/r , v is the speed and r is the radius. The centripetal force would be Fc = m *v^2/r. Now, if v = c, the speed of light, then Fc = E/r, and for a 1kg object the force needed would be 300 GN or 67.4 Giga-pounds of force (4.448 newtons are in a pound).
That is a a lot. An elephant has 50kN force (gravity) so you would need a force equal to 6 million elephants to do that job. But there is more: Derek calculated that at 30 m from the center of rotation, the arm would need to have a base as big as the observable universe in order to support that kind of force. And there is the inertia we need to fight when we need to accelerate the arm from one speed to another so the arm, the tether, would have to be thicker. If you are at 99% the speed of light and you want to accelerate the arm to 100% the speed of light, then you would need an infinite amount of energy.
Lastly, the arm is kept together by the electromagnetic force so the particles from within cannot communicate with each other faster than the speed of light. Since the particles communicate using electromagnetic waves ie light ie photons, the maximum speed in those arms is the speed of light (and of course the force will only be transmitted as fast as the speed of sound in it, see above). So, nope. Nothing can go faster than the speed of light.