From: tjroberts137@sbcglobal.net   
      
   On 9/29/17 9/29/17   8:20 AM, John Heath wrote:   
   > A car is moving at .1 c.   
      
   RELATIVE TO THE ROAD. When you don't specify which frame you are using you   
   only confuse yourself (and any readers). Here we presume the road is at rest in   
   an inertial frame.   
      
   	Compared to a car at 0.1 c, the earth's rotation and orbital   
   	speed are negligible. Not to mention that it would launch into   
   	space. So assume a flat road sufficiently long.   
      
   > The tire on the road at 6:00 o'clock , bottom , is moving at 0 c as it is   
   > touching the road but at 12:00 o'clock , top , the tire is moving at .2 c   
   > twice as fast as the car. Does this mean the car is limited to speed .5 c as   
   > at this speed the top of the tire will be moving at c twice as fast as the   
   > car ?   
      
   No. You have assumed Galilean relativity, in which velocities add vectorially.   
   That does not correspond to the world we inhabit.   
      
   You must use the Lorentz composition of velocities: Both points of the tire are   
   moving at 0.1 c relative to the axle (in opposite directions), and the axle is   
   moving at 0.1 c relative to the road (along with the rest of the car except its   
   wheels/tires). So the top of the tire is moving at this speed relative to the   
   road:   
   	v = (v1 + v2) / (1 + v1 * v2 / c^2)   
   	v = (0.1 c + 0.1 c) / (1 + 0.1 * 0.1) = 0.198 c   
      
   If the car moves at 0.5 c relative to the road, the top of the tire moves at   
   this speed relative to the road:   
   	v = (0.5 c + 0.5 c) / (1 + 0.5 * 0.5) = 0.8 c   
      
   If the car moves at 0.99 c relative to the road, the top of the tire moves at   
   this speed relative to the road:   
   	v = (0.99 c + 0.99 c) / (1 + 0.99 * 0.99) = 0.9999 c   
      
   For all car speeds relative to the road that are less than c, the top of the   
   tire also moves relative to the road at a speed less than c.   
      
   	Note I have ignored the impossibility of such speeds using tires   
   	-- no material is anywhere close to strong enough to sustain   
   	the strain induced by such enormous rotational velocities.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
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