Question
Derive the relations
  1. $\text{L}=\text{I}\omega$
  2. $\tau=\text{I}\alpha$

Answer

  1. To prove $\text{L}=\text{I}\omega$

We know, L = r × p = r × mv

$=\text{rmr}\omega=\text{mr}^2\omega=\text{I}\omega$

  1. 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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