Shutterstock/Holly Michele
Last Word is Â鶹´«Ã½’s long-running series in which readers give scientific answers to each other’s questions, ranging from the minutiae of everyday life to absurd astronomical hypotheticals. To answer a question or ask a new one, email lastword@newscientist.com
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? (continued)
Ron Dippold
San Diego, California, US
Sadly, a disc could never approach the speed of light. If you had a high-strength steel disc that was 1-metre thick and 1 kilometre in diameter, it would come apart from centrifugal force at just 11 revolutions per minute or so. Even if the disc were made from the strongest possible diamond, you could only get the rim up to 8.6 kilometres per second (164 revolutions per minute) before it shattered. The material with the highest theoretical tensile strength is carbyne, a form of carbon estimated to be up to three times as strong as the strongest possible diamond. That would reach 26 km/s before shattering.
What if you took a neutron star and made a disc out of it? Without being a sphere, it would fall apart, but assuming you could somehow keep it as dense as a neutron star, even at the most extreme density estimates of 300 quadrillion times stronger than carbyne, you could only get the rim up to about 900 km/s (3/1000th the speed of light) before it broke, because the strength scales with the square root.
Well, let’s set all that aside and assume the disc is made of infinitely strong handwavium, which happens to be as dense as diamond. To pump enough energy in to get the rim up to 99 per cent the speed of light, you would need about 200 septillion joules. That sounds huge, but it is “only” about 35 years of all the solar power reaching Earth.
Going back to our 1-metre-thick disc, if you or I were at the rim, we would be instantly squished to single atom thickness or flung off into the far reaches of space by centrifugal force. If we handwave some more and say we could survive at the rim, you would see strong time dilation: 1 minute for us there would be 7 minutes on Earth. But would that really be worth stealing all Earth’s energy for 35 years?
Mike Follows
Sutton Coldfield, West Midlands, UK
No very large disc could ever spin anywhere near the speed of light before falling apart, as the atomic bonds simply aren’t strong enough, so pieces would fly off the edge once the stress became too great.
Smaller objects can spin much faster before breaking. Take a silica nanoparticle, just 150 nanometres across: scientists have spun one at over 300 million revolutions per minute. Even at that incredible angular speed, its circumference was moving at only a few metres per second – a consequence of its tiny size.
Interestingly, the maximum rim speed depends on the material, not the size of the disc. Steel can only manage around 500 metres per second, whereas graphene could reach nearly 8000 metres per second, thanks to its exceptional strength and low density.
Switching from a disc to a cylinder doesn’t help much – in fact, it would result in the object falling apart at an even lower rotational speed. A rotating space habitat based on an O’Neill cylinder would need to be spun fast enough so that people walking around on its inner surface would experience the same force of gravity that we feel on Earth’s surface. However, comfort dictates that the spin rate should be less than 1 revolution per minute, which requires a radius of at least 1 kilometre, although the maximum size is ultimately limited by the material’s strength.
“
No disc could ever spin anywhere near the speed of light before falling apart – the atomic bonds simply aren’t strong enough
“
To answer this question – or ask a new one – email lastword@newscientist.com.
Questions should be scientific enquiries about everyday phenomena, and both questions and answers should be concise. We reserve the right to edit items for clarity and style. Please include a postal address, daytime telephone number and email address.
Â鶹´«Ã½ retains total editorial control over the published content and reserves all rights to reuse question and answer material that has been submitted by readers in any medium or in any format.
