Aristotle's wheel [duplicate]
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This question already has an answer here:
Satisfying explanation of Aristotle's Wheel Paradox.
3 answers
two wheels of different diameter attached to each other at the center, roll along a straight line. since they have different diameters, the smaller wheel must slip. (see other stackexchange answers)
Why do I not see the slippage in these videos: https://www.youtube.com/watch?v=mW-0bZwoGwQ
https://www.youtube.com/watch?v=mmBx8HW6qkQ ?
physics paradoxes
asked Dec 27 '18 at 10:11
george sgeorge s
32
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marked as duplicate by Peter, José Carlos Santos, Mauro ALLEGRANZA, Davide Giraudo, mrtaurho Dec 27 '18 at 12:36
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Satisfying explanation of Aristotle's Wheel Paradox.
3 answers
two wheels of different diameter attached to each other at the center, roll along a straight line. since they have different diameters, the smaller wheel must slip. (see other stackexchange answers)
Why do I not see the slippage in these videos: https://www.youtube.com/watch?v=mW-0bZwoGwQ
https://www.youtube.com/watch?v=mmBx8HW6qkQ ?
physics paradoxes
asked Dec 27 '18 at 10:11
george sgeorge s
32
$endgroup$
marked as duplicate by Peter, José Carlos Santos, Mauro ALLEGRANZA, Davide Giraudo, mrtaurho Dec 27 '18 at 12:36
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
Satisfying explanation of Aristotle's Wheel Paradox.
3 answers
two wheels of different diameter attached to each other at the center, roll along a straight line. since they have different diameters, the smaller wheel must slip. (see other stackexchange answers)
Why do I not see the slippage in these videos: https://www.youtube.com/watch?v=mW-0bZwoGwQ
https://www.youtube.com/watch?v=mmBx8HW6qkQ ?
physics paradoxes
asked Dec 27 '18 at 10:11
george sgeorge s
32
$endgroup$
This question already has an answer here:
Satisfying explanation of Aristotle's Wheel Paradox.
3 answers
two wheels of different diameter attached to each other at the center, roll along a straight line. since they have different diameters, the smaller wheel must slip. (see other stackexchange answers)
Why do I not see the slippage in these videos: https://www.youtube.com/watch?v=mW-0bZwoGwQ
https://www.youtube.com/watch?v=mmBx8HW6qkQ ?
This question already has an answer here:
Satisfying explanation of Aristotle's Wheel Paradox.
3 answers
physics paradoxes
physics paradoxes
asked Dec 27 '18 at 10:11
george sgeorge s
32
asked Dec 27 '18 at 10:11
george sgeorge s
32
asked Dec 27 '18 at 10:11
george sgeorge s
32
asked Dec 27 '18 at 10:11
george sgeorge s
32
asked Dec 27 '18 at 10:11
george sgeorge s
32
32
marked as duplicate by Peter, José Carlos Santos, Mauro ALLEGRANZA, Davide Giraudo, mrtaurho Dec 27 '18 at 12:36
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Peter, José Carlos Santos, Mauro ALLEGRANZA, Davide Giraudo, mrtaurho Dec 27 '18 at 12:36
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
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The fact that you don't see any slippage does not mean that it's not there.
In the video you see two fixed lines, $a$ (the big circle is rolling along it) and line $b$ which is there just for orientation. If the velocity of circle center $A$ is $v_A$, the velocity $v_B$ of point $B$ currently in touch with line $b$ is much smaller but it's still different to zero (see picture). There is no slippage only if the touching point has velocity equal to zero, which is true for $P_v$ but not for $B$. Therefore, the smaller circle does not roll along the line $b$ without slippage. It's there, it's just hard to spot it because of much smaller magnitude of velocity $v_B$.
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
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but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
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– george s
Dec 27 '18 at 12:04
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
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– Oldboy
Dec 27 '18 at 12:12
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aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
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– george s
Dec 27 '18 at 13:01
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@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
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I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
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– george s
Dec 27 '18 at 14:44
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The fact that you don't see any slippage does not mean that it's not there.
In the video you see two fixed lines, $a$ (the big circle is rolling along it) and line $b$ which is there just for orientation. If the velocity of circle center $A$ is $v_A$, the velocity $v_B$ of point $B$ currently in touch with line $b$ is much smaller but it's still different to zero (see picture). There is no slippage only if the touching point has velocity equal to zero, which is true for $P_v$ but not for $B$. Therefore, the smaller circle does not roll along the line $b$ without slippage. It's there, it's just hard to spot it because of much smaller magnitude of velocity $v_B$.
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
$endgroup$
$begingroup$
but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
$endgroup$
– george s
Dec 27 '18 at 12:04
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
$endgroup$
– Oldboy
Dec 27 '18 at 12:12
$begingroup$
aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
$endgroup$
– george s
Dec 27 '18 at 13:01
$begingroup$
@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
$begingroup$
I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
$endgroup$
– george s
Dec 27 '18 at 14:44
add a comment |
$begingroup$
The fact that you don't see any slippage does not mean that it's not there.
In the video you see two fixed lines, $a$ (the big circle is rolling along it) and line $b$ which is there just for orientation. If the velocity of circle center $A$ is $v_A$, the velocity $v_B$ of point $B$ currently in touch with line $b$ is much smaller but it's still different to zero (see picture). There is no slippage only if the touching point has velocity equal to zero, which is true for $P_v$ but not for $B$. Therefore, the smaller circle does not roll along the line $b$ without slippage. It's there, it's just hard to spot it because of much smaller magnitude of velocity $v_B$.
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
$endgroup$
$begingroup$
but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
$endgroup$
– george s
Dec 27 '18 at 12:04
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
$endgroup$
– Oldboy
Dec 27 '18 at 12:12
$begingroup$
aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
$endgroup$
– george s
Dec 27 '18 at 13:01
$begingroup$
@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
$begingroup$
I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
$endgroup$
– george s
Dec 27 '18 at 14:44
add a comment |
$begingroup$
The fact that you don't see any slippage does not mean that it's not there.
In the video you see two fixed lines, $a$ (the big circle is rolling along it) and line $b$ which is there just for orientation. If the velocity of circle center $A$ is $v_A$, the velocity $v_B$ of point $B$ currently in touch with line $b$ is much smaller but it's still different to zero (see picture). There is no slippage only if the touching point has velocity equal to zero, which is true for $P_v$ but not for $B$. Therefore, the smaller circle does not roll along the line $b$ without slippage. It's there, it's just hard to spot it because of much smaller magnitude of velocity $v_B$.
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
$endgroup$
The fact that you don't see any slippage does not mean that it's not there.
In the video you see two fixed lines, $a$ (the big circle is rolling along it) and line $b$ which is there just for orientation. If the velocity of circle center $A$ is $v_A$, the velocity $v_B$ of point $B$ currently in touch with line $b$ is much smaller but it's still different to zero (see picture). There is no slippage only if the touching point has velocity equal to zero, which is true for $P_v$ but not for $B$. Therefore, the smaller circle does not roll along the line $b$ without slippage. It's there, it's just hard to spot it because of much smaller magnitude of velocity $v_B$.
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
answered Dec 27 '18 at 11:31
OldboyOldboy
8,4621936
8,4621936
$begingroup$
but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
$endgroup$
– george s
Dec 27 '18 at 12:04
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
$endgroup$
– Oldboy
Dec 27 '18 at 12:12
$begingroup$
aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
$endgroup$
– george s
Dec 27 '18 at 13:01
$begingroup$
@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
$begingroup$
I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
$endgroup$
– george s
Dec 27 '18 at 14:44
add a comment |
$begingroup$
but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
$endgroup$
– george s
Dec 27 '18 at 12:04
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
$endgroup$
– Oldboy
Dec 27 '18 at 12:12
$begingroup$
aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
$endgroup$
– george s
Dec 27 '18 at 13:01
$begingroup$
@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
$begingroup$
I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
$endgroup$
– george s
Dec 27 '18 at 14:44
$begingroup$
but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
$endgroup$
– george s
Dec 27 '18 at 12:04
$begingroup$
but in the video clips the two wheels are connected rigidly. Nevertheless, they arrive at the same point ofter one revolution. I understand there MUST be slippage but how can they slip relative to each other since they are connected rigidly?
$endgroup$
– george s
Dec 27 '18 at 12:04
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
$endgroup$
– Oldboy
Dec 27 '18 at 12:12
$begingroup$
This is not about slippage between points on the big and the small circle. This is about rolling slippage (sliding) that exists between point $B$ on the small circle and line $b$. Bacause of that sliding at point $B$ between the small circle and the line $b$, you cannot say that circumference of the small circle is equal to the distance travelled by the center of the wheel. It's like a car wheel slipping on an icy road. The center of the wheel is fixed but the points on the tyre are passing great distances.
$endgroup$
– Oldboy
Dec 27 '18 at 12:12
$begingroup$
aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
$endgroup$
– george s
Dec 27 '18 at 13:01
$begingroup$
aha, so they don't slip relative to each other, but the larger wheel rolls along line a, while the smaller one 'rolling slips' relative to the (imaginary) line b. And it does so continuously which is why this cannot be observed in the video. Correct? thank you!
$endgroup$
– george s
Dec 27 '18 at 13:01
$begingroup$
@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
$begingroup$
@georges Exactly, now you have it 100% right :) If satisifed, please upvote and/or accept the answer :)
$endgroup$
– Oldboy
Dec 27 '18 at 14:06
$begingroup$
I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
$endgroup$
– george s
Dec 27 '18 at 14:44
$begingroup$
I tried to upvote but apparently, since I am a newbie, my vote is "recorded but not displayed"
$endgroup$
– george s
Dec 27 '18 at 14:44
add a comment |
