anonymous
  • anonymous
I have a stick spinning around a perpendicular axis in the center. What's its rotational inertia?\[\int r^2\,dm\]?
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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JamesJ
  • JamesJ
That is the definition of the moment of inertia. The trick now is the evaluate that integral. If the stick is of length a and uniform mass density with a total mass m, then \[ dm = \frac{m}{a} dr \] and the moment of inertia is \[ I = \int_{-a/2}^{a/2} \frac{m}{a} r^2 dr \] Now evaluate.
anonymous
  • anonymous
Can you run me through how we arrived at \[dm=\frac{m}{a}dr\]?

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