Question

state the law of conservation of angular momentum,write its mathematical form.

Answer 1

$$\begin{gathered} \mathbf{Law}\mathbf{}\mathbf{of}\mathbf{}\mathbf{conservation}\mathbf{}\mathbf{of}\mathbf{}\mathbf{angular}\mathbf{}\mathbf{momentum}\mathbf{:} \\ \mathrm{In}\mathrm{the}\mathrm{absence}\mathrm{of}\mathrm{net}\mathrm{external}\mathrm{torque}\mathrm{of}\mathrm{a}\mathrm{system}\mathrm{about}\mathrm{the}\mathrm{given}\mathrm{axis},\mathrm{the}\mathrm{angular}\mathrm{momentum} \\ \mathrm{of}\mathrm{the}\mathrm{system}\mathrm{remains}\mathrm{constant}\mathrm{about}\mathrm{that}\mathrm{axis}. \\ \mathbf{Mathematical}\mathbf{}\mathbf{notation}\mathbf{:} \\ \mathrm{If}\sum _{}^{}\mathrm{\tau }=0,\mathrm{then}\stackrel{\rightharpoonup }{\mathrm{L}}=\mathrm{constant}\left(\mathrm{or}\right)\mathrm{I}\times \stackrel{\rightharpoonup }{\mathrm{\omega }}=\mathrm{constant} \end{gathered}$$