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The SAT Problem That Everybody Got Wrong
- wrycoder 3y agoEr, this is easy. By the time it rotates 90 degrees, it's upside down. So, two full turns.
- psychphysic 3y agoScientific American is on the same trajectory as the History channel. I'm just assuming this is clickbait and will keep an eye out for the archive link.
- assbuttbuttass 3y agoI found it helpful to imagine the picture after the smaller coin has made one full rotation. Let x be the angle that we have traveled along the larger coin. Now we notice there's some similar triangles, and x is also the angle that we have left to travel on the smaller coin. I.e. we traveled 2pi - x on the smaller coin. But we know the edges were touching, so the arclength of these two angles must be equal. 3x = 2pi - x x = pi/2 So going around the whole way, you can do 2pi/x = 4 rotations
- entropicgravity 3y agoIf you use the center of the smaller rotating circle rather than where it touches the larger circle then it all works out. Hindsight is 20/20.
- School-Cotton 3y agoA problem with a similar flavor: how long does it take the earth to rotate once on its axis? The answer is about 23h56m. However, after that time, the earth has also moved slightly relative to the sun, so it takes another four minutes for the earth to rotate enough such that the sun is at the same point in the sky as it started at. Hence why we consider a day to be 24h.
- euroderf 3y agoAnd 365 days x ~4 minutes = ~1460 minutes, i.e. 24 hours. And in a year, the Earth rotates on its axis ~366 times ?
- School-Cotton 3y ago> And in a year, the Earth rotates on its axis ~366 times ? Yes, exactly.
- boneitis 3y agoI never pass up the opportunity to use the couple of cool words whenever this topic crops up. It is the distinction between a solar day and a sidereal day. :)