Confused while reading HRK regarding rotational kinematics

In summary, the discussion revolves around the axis of rotation for a chimney and its intended rotation. The author suggests that the axis of rotation should be perpendicular to the ground and go through the center of the chimney. However, since the text mentions the length of the chimney, the intended rotation may be parallel to the ground. The conversation ends with the realization that the chimney may not be able to rotate in the intended manner due to its shape.
  • #1
Afo
17
5
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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  • #2
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?
 
  • #3
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?
 
  • #4
No the axis of (this specific rotation shown in the picture) rotation is not the axis of the chimney. Think again please.
 
  • #5
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: )
 
  • #6
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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  • #7
PeroK said:
You mean the chimney should be doing something like this?
That would be one amazing chimney! :biggrin:
 
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  • #8
Doc Al said:
That would be one amazing chimney! :biggrin:
And one amazing explosives expert!
 
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  • #9
Oh never mind. I got it. I kinda misunderstood what a chimney is. Here's the picture explaining everything:
Jp7Dn0J.png
 

FAQ: Confused while reading HRK regarding rotational kinematics

What is rotational kinematics?

Rotational kinematics is the study of the motion of objects that are rotating or moving in a circular path. It involves analyzing the position, velocity, and acceleration of these objects as they rotate.

How is rotational kinematics different from linear kinematics?

Rotational kinematics deals with the motion of objects in circular paths, while linear kinematics deals with the motion of objects in straight lines. The equations and principles used to analyze rotational motion are different from those used in linear motion.

What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed axis. It is usually measured in radians per second and is represented by the symbol ω.

How is torque related to rotational kinematics?

Torque is the force that causes an object to rotate. It is directly related to rotational kinematics because it affects an object's angular acceleration, which in turn affects its rotational motion.

What are some real-world applications of rotational kinematics?

Rotational kinematics is used in many real-world applications, such as understanding the motion of planets and other celestial bodies, designing and analyzing machinery and vehicles that involve rotating parts, and studying the motion of fluids in circular containers.

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