An earth has a mass m and moves with angular momentum L.its areal velocity is given by.........
An earth has a mass m and moves with angular momentum L.its areal velocity is given by.........
RishiKesh Rubhan , 11 Years ago
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General Physics> An earth has a mass m and moves with angu...
1 AnswersAbhishek Kumar
The areal velocity vector is
![\frac{d \vec{A}}{d t} = \lim_{\Delta t \rightarrow 0} {\Delta \vec{A} \over \Delta t} = \lim_{\Delta t \rightarrow 0} {\vec{r}(t) \times \vec{r}(t + \Delta t) \over 2 \Delta t} = \lim_{\Delta t \rightarrow 0} {\vec{r}(t) \times [ \vec{r}(t) + \vec{r}\,'(t) \Delta t ] \over 2 \Delta t} = \lim_{\Delta t \rightarrow 0} {\vec{r}(t) \times \vec{r}\,'(t) \over 2} \left( {\Delta t \over \Delta t} \right) = {\vec{r}(t) \times \vec{r}\,'(t) \over 2}. But, \frac{d \vec{A}}{d t} = {\vec{r} \times \vec{v} \over 2}. so, Areal velocity = L/2m](https://files.askiitians.com/cdn1/cms-content/common/latex.codecogs.comgif.latex_fracd_vecadt_lim__deltat_rightarrow0_delta_veca_over_deltat_lim__deltat_rightarrow0_vecrt_times_vecrt_deltat_over2_deltat_lim__deltat_rightarrow0_vecrt_times_vecrt_vecr_t_deltat_over2_deltat_lim__deltat_rightarrow0_vecrt_times_vecr_t_over2_left_deltat_over_deltat_right_vecrt_times_vecr_t_over2.but_fracd_vecadt_vecr_times_vecv_over2.soarealvelocityl2m.jpg)
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