Angular Momentum Problem: Rotation Rate

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Homework Help Overview

The discussion revolves around a problem related to angular momentum and rotation rates, specifically focusing on the calculation of moment of inertia and its application in determining rotation rates about the z-axis.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculation of moment of inertia and its application in the context of angular momentum. Questions arise regarding the distances from the z-axis and the interpretation of the unit vector ##\hat k##. There is also mention of using the Pythagorean theorem to find distances from the z-axis.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and clarifying concepts related to the z-axis and distances. Some guidance has been offered regarding the use of the Pythagorean theorem, but no consensus has been reached on the correct approach or solution.

Contextual Notes

There appears to be confusion regarding the definitions of distances in relation to the z-axis and the application of the moment of inertia in the context of angular momentum calculations. Participants are questioning assumptions about the setup of the problem.

JoeyBob
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Homework Statement
See attached
Relevant Equations
L=rotation rate*I
First I found the moment of inertia,

I=1.8(5.5^2+3.9^2+4.9^2)

=125.046

Then I tried to find the rotation rate using the equation L=rotation rate*I

rotation rate=3773/125.046=30.173

But the answer is suppose to be 21.263?
 

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JoeyBob said:
First I found the moment of inertia,

I=1.8(5.5^2+3.9^2+4.9^2)
No. The rotation is about the z (k) axis. What are the distances from that axis?
 
haruspex said:
No. The rotation is about the z (k) axis. What are the distances from that axis?

Doesn't k hat represent how far something is from the z axis?
 
JoeyBob said:
Doesn't k hat represent how far something is from the z axis?
No, it is how far it is along the z axis. And you mean the coefficient of ##\hat k##. ##\hat k## is the direction of the z axis.
 
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You have to use pythagorean theorem on the i and j coordinates to find the distance from the z-axis.
 
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haruspex said:
No, it is how far it is along the z axis. And you mean the coefficient of ##\hat k##. ##\hat k## is the direction of the z axis.
Delta2 said:
You have to use pythagorean theorem on the i and j coordinates to find the distance from the z-axis.
Yes.
 

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