Question
Derive the relations
- $\text{L}=\text{I}\omega$
- $\tau=\text{I}\alpha$
To prove $\text{L}=\text{I}\omega$
We know, L = r × p = r × mv
$=\text{rmr}\omega=\text{mr}^2\omega=\text{I}\omega$
To prove $\tau=\text{I}\alpha$
We know, $\tau=\text{r F}=\text{rma}$
$=\text{mr}^2\alpha=\text{I}\alpha$
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