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wrote...
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A month ago
Hope this makes sense...  A physics teacher of mine stated to the whole class that the outside of a clock-hand moves at greater velocity than the inside and one of the students questioned this by saying something like, if that is the case then why do all parts of the clock-hand make one revolution in the same time. 
He also said that the outside of the clock-hand was not therefor moving at greater velocity, but that it was merely moving with greater angular momentum due to an increase in mass towards the outside and that this makes it seem as though the outside of the hand is going faster but isn't actually the case.
My question is was the teacher correct or the pupil?
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wrote...
A month ago
Technically the tip does move faster than the base. All points in the hand make one revolution in the same amount of time. In that time, the tip traces out a circle with a larger circumference than any other part which is closer to the center. If the tip travels a longer distance in the same amount of time, then it must have been moving faster.
wrote...
A month ago Edited: A month ago, ajac63
This would seem to be the case and of course you could apply the same pros and cons to a roundabout; the outside seems to be going faster than the inside because it's covering a greater distance in the same time, however I personally think that the counter argument has some merit. There is an increase in mass the further away you get from the centre and so greater angular momentum which we would perceive as greater velocity, but as all parts of the clock-hand (or roundabout) are making one revolution in the same time, is this the case?
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wrote...
Staff Member
A month ago
Both are great arguments, but for me it's easier to wrap my head around the first one. That is, the tip makes a longer run in the same amount of time, therefore it's faster. I also like the notion that there's more weight to be pulled closer to the center than further away, so greater angular momentum. Can that be quantified mathematically?
- Master of Science in Biology
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wrote...
4 weeks ago
Sorry for late response, blame my ISP  Face with Stuck-out Tongue 

Whether or not this can be quantified mathematically I don't know, although I'm sure this has been done, but however one looks at this, it is a bit of a conundrum or puzzle. 

On the one hand greater distance is covered the further out you go, and so yes, an increase in velocity would seem to be the case, but on the other hand all of the hand (or roundabout) makes one revolution in the same time. 
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Educator
3 weeks ago Edited: 3 weeks ago, bio_man
but on the other hand all of the hand (or roundabout) makes one revolution in the same time.

The tip of hand moves faster because it has faster linear velocity, but the angular velocity is the same. Wherever the reference point along the arm, the # of revolutions are the same, but the displacement will be different depending on the length. I don't think this is a conundrum, because it adds up nicely.

Want a stranger conundrum, try wrapping your head around this: https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF

The sum of a series of natural numbers 1 + 2 + 3 + 4 ... diverges to -1/12... Grinning Face with Smiling Eyes
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