Question

Obtain an expression for acceleration of a performing uniform circular motion.

Answer 1

as we know centripetal force, when body perform circular motion

$F_c=\frac{m{v}^2}{r}$

$m{a}_c=\frac{m{v}^2}{r}$

from above equation we can say,

$a_r=\frac{V^2}{r}$

$a_T=\frac{dV}{dt}$

$\because$ $\frac{d\overrightarrow{V}}{dt}=0$ (uniform motion)

$\therefore$ ${\overrightarrow{a}}_{Total}={\overrightarrow{a}}_r=\frac{V^2}{r}(-\hat{r})$