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If a very large disc on a frictionless, horizontal spindle were gradually rotated faster and faster, what would happen as the rim approached the speed of light?
Mel Earp
Macclesfield, Cheshire, UK
I am always drawn to the Large Hadron Collider when considering questions like this. The LHC has a diameter of about 8.5 kilometres. When operating, it uses the equivalent of about a third of the energy required by the nearby city of Geneva. This is mostly consumed by the many large magnets needed to keep the beams, usually protons, in a circle.
There can be about 300 trillion protons in the collider at any time. This gives a mass of about 5 × 10-13 kilograms, which is tiny and yet requires so much energy to constrain.
No known material has the tensile strength to match. As a result, the rim of a spinning disc would detach long before approaching the speed of light. If acceleration were to continue, so would the disintegration.
However, imagine there were such a material. Then we get into the deep waters of special relativity, where the circumference experiences length contraction from the perspective of a stationary observer, but the radius doesn’t, seemingly breaking the geometrical relationship between the radius and the circumference.
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The rim of a spinning disc would detach long before the speed of light. If acceleration continued, so would the disintegration
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Let’s just be content that it isn’t possible to construct this disc!
Ian Roselman
Leighton Buzzard, Bedfordshire, UK
Many years ago, when I was a research student in the physics department at the University of Cambridge, I was shown a room with bits of metal embedded in the walls. I was told that this was where a steel ball had been spun inside a glass vacuum jar at ever increasing speed, controlled by magnetic forces. Long before the peripheral speed of the ball came anywhere near the speed of light, the ball burst, shattered the jar and peppered the walls with metal.
Fortunately, the walls were thick and nobody was in the room at the time. This disintegration happened because the centrifugal force felt by the outer layers of atoms in the ball finally overcame the cohesive force of the metal. Similarly, I have calculated that a wheeled vehicle can’t travel much faster than 1600 kilometres per hour before the wheels succumb to this effect.
Richard Waspe
Norwich, Norfolk, UK
Under increasing force, the disc’s edge would distort more and more with ever faster rotation, eventually assuming a circumference not related to pi and not conforming to Euclidean geometry. In the real world, the disc would disintegrate long before this. However, if you were sitting on the disc – and not getting ill or squashed – your own part of the disc would appear unchanged. It’s all relative…
Dave Neale
Bedford, UK
It can’t. The frictionless spindle is irrelevant. Centrifugal force will tear apart any spinning object at a tiny fraction of the speed of light.
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