Imagine a record on a record player. There is a dot near the outer edge and a dot near the inner edge. Like this:

The whole record is spinning at 45 revolutions per minute. However, the outer dot has to travel farther around than the inner dot. This means that in order to stay in line with the inner dot, the outter dot has to travel faster. But both dots are moving at 45 rpm, so how can one be traveling slower than the other?

Ugh, so much lost sleep...
one revolution is less distance for the smaller dot, so although they're moving at the same rpm they're going at different speeds. but that doesn't make sense. OMFG THE SKY IS FALLING!!!!
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rpm is nothing to do with speed, the outside dot travels quicker but has the same amount of complete revolutions in the same time
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RPM is angular velocity which they both have the same of, 45 rpm, but their linear velocity is different.
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RPM is angular velocity which they both have the same of, 45 rpm, but their linear velocity is different.

exactly. to threadstarter, this really isnt that difficult to underestand, think about how gearing works in your bicycle as another example...
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rpm is not a measurement of speed. The statement "both dots are moving at 45 rpm" is nonsense. Obviously, the 2 dots move at different speeds, with the one at the edge being faster since it has a longer distance to travel in the time of a single revolution.
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Just think of an angle. Make 2 lines intersect eachother.
There is less distance between the 2 lines the closer you are to the intersection.
They both have the same RPM. But the outer dot is moving faster AND farther, but theyre both moving around the same point.

So as the RPM stays the same, the speed and distance(radius) are related (as distance increases, so does speed).

Im sure theres some simple equation to show you but im too lazy to figure it out...
yeah this isnt really a paradox, its pretty simple physics, i did problemslike this in middle school.
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basic physics...both have the same angular speed of 45 rpm. however, their linear speed (or tangential speed) is different. conveniently enough, the two are related by an equation, where v is linear speed, r is the radius of something (in the case of the record, one of the dots), and w (actually, it's omega, but it looks like a w) is the angular speed:

v = r * w

problem solved.
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yea seriously threadstarter got fucked

it's not that hard to work out though.

You're so hardcore.