Confused while reading HRK regarding rotational kinematics

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Homework Help Overview

The discussion revolves around understanding rotational kinematics in the context of a chimney's axis of rotation. Participants are trying to clarify the relationship between the chimney's dimensions and its rotational behavior.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the correct axis of rotation for the chimney, questioning whether it should be based on the radius or the length. There is a back-and-forth regarding the orientation of the chimney and its implications for rotation.

Discussion Status

Some participants have offered hints and suggestions about the axis of rotation, while others express confusion about the chimney's orientation and its implications for the problem. Multiple interpretations of the axis of rotation are being explored without reaching a consensus.

Contextual Notes

There is mention of the chimney starting in a vertical position, which may influence the understanding of its rotational dynamics. Participants are also considering the implications of the chimney being intact versus destroyed.

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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