Confused while reading HRK regarding rotational kinematics

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SUMMARY

The discussion centers on the confusion surrounding the axis of rotation in the context of rotational kinematics as it pertains to a chimney. Participants clarify that the axis of rotation is perpendicular to the ground and passes through the chimney's center, which is multiplied by the chimney's radius. The text also suggests that the intended axis of rotation is parallel to the ground, leading to further confusion about the actual mechanics involved. Ultimately, the conversation emphasizes the importance of accurately interpreting the axis of rotation in relation to the chimney's physical properties.

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Afo
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Homework Statement
Refer to the two pictures which are from Halliday Resnick Krane Physics 1 about rotational kinematics:

I am confused why the tangential acceleration, $a_T$, is alpha (angular acceleration) times the length of the chimney, L.

My thinking is that it should be the radius of the chimney and not the length of the chimney
Relevant Equations
a_t = \alpha \cdot r
Pic 1:

Pic 2:
 
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Afo said:
My thinking is that it should be the radius of the chimney and not the length of the chimney
What's the axis of rotation?
 
Assuming that the chimney is not destroyed yet, the axis of rotation is perpendicular to the ground and goes through the center of the chimney. However, this means that it's multiplied by the radius.

However, since the text mentions the length of the chimney, the author's intended axis of rotation would be parallel to the ground. But I don't see anything rotating with respect to that axis
Doc Al said:
What's the axis of rotation?
 
No the axis of (this specific rotation shown in the picture) rotation is not the axis of the chimney. Think again please.
 
Afo said:
However, since the text mentions the length of the chimney, the author's intended axis of rotation would be parallel to the ground. But I don't see anything rotating with respect to that axis
Hint: The chimney started out vertical. (Presumably. :wink: )
 
Afo said:
Assuming that the chimney is not destroyed yet, the axis of rotation is perpendicular to the ground and goes through the center of the chimney. However, this means that it's multiplied by the radius.

However, since the text mentions the length of the chimney, the author's intended axis of rotation would be parallel to the ground. But I don't see anything rotating with respect to that axis
You mean the chimney should be doing something like this?

 
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PeroK said:
You mean the chimney should be doing something like this?
That would be one amazing chimney! :biggrin:
 
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Doc Al said:
That would be one amazing chimney! :biggrin:
And one amazing explosives expert!
 
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Oh never mind. I got it. I kinda misunderstood what a chimney is. Here's the picture explaining everything:
Jp7Dn0J.png
 

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