- #1
soopo
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Homework Statement
Show that the moment of inertia of a disk is [itex] 0.5 mr^2 [/itex].
The Attempt at a Solution
[tex] I = \int R^2 dm [/tex]
Using [itex] dm = \lambda dr [/itex] such that [itex] m = \lambda r [/itex]:
[tex] = \int_{-r}^{r} R^2 \lambda dr [/tex]
[tex] = \frac { \lambda } {3} ( 2r^3 ) [/tex]
[tex] = \frac {2} {3} (\lambda r ) (r^2) [/tex]
[tex] = \frac {2} {3} M R^2 [/tex]
which should be the moment of inertia for a ring.
Integrating this from 0 to 2pii relative to the angle gives me [itex] \frac {4} {9} m r^3 [/tex],
which is wrong.
How can you calculate the moment of inertia for a disk?