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If I take a dumbbell with one end on the radius of a circle ( and a little away from the centre) and the other other end also along the same radius and rotate the dumbbell about the centre. Let the speed of the nearer end be c/9 then there may be a situation with the farther end traveling at a speed more than c?

ACB
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Harsh Anand
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It is physically possible to get the end at smaller radius to travel at $c/9$. If the dumbbell stayed straight and its end were at ten times the radius and then that end would be moving at $10 c / 9$ but this situation is not physically possible. As you tried to get the farther end of the dumbbell to move that fast you would be trying to get its momentum to increase and as its speed approached $c$ the momentum would approach infinity. No force will be large enough to do it.

So what would really happen in an experiment where you tried to get such a dumbbell to swing more and more quickly? Eventually something would give: either the dumbbell would bend or it would break.

There is a wider lesson here about rigid motion in relativity: rigid rotation is not possible for objects of large radius.

Andrew Steane
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